UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM N-CSR

CERTIFIED SHAREHOLDER REPORT OF REGISTERED
MANAGEMENT INVESTMENT COMPANIES

ITEM 1. REPORT TO STOCKHOLDERS.

The Annual Report to Stockholders is filed herewith.

Annual Report

Western Asset Global High Income Fund Inc.

(EHI)

Fund objectives

The Fund’s primary investment objective is high current income. The Fund’s secondary investment objective is total return.

What’s inside

Dear Shareholder,

We are pleased to provide the annual report of Western Asset Global High Income Fund Inc. for the twelve-month reporting period ended May 31, 2012. Please read on for a detailed look at prevailing economic and market conditions during the Fund’s reporting period and to learn how those conditions have affected Fund performance.

As always, we remain committed to providing you with excellent service and a full spectrum of investment choices. We also remain committed to supplementing the support you receive from your financial advisor. One way we accomplish this is through our website, www.lmcef.com. Here you can gain immediate access to market and investment information, including:

·             Fund prices and performance,

·             Market insights and commentaries from our portfolio managers, and

·             A host of educational resources.

We look forward to helping you meet your financial goals.

Sincerely,

R. Jay Gerken, CFA

Chairman, President and Chief Executive Officer

June 29, 2012

Investment commentary

Economic review

The U.S. economy continued to grow over the twelve months ended May 31, 2012, albeit at an uneven pace. U.S. gross domestic product (“GDP”)i growth, as reported by the U.S. Department of Commerce, was 1.3% and 1.8% in the second and third quarters of 2011, respectively. The economy then gathered further momentum late in 2011, as the Commerce Department reported that fourth quarter GDP growth was 3.0% — the fastest pace since the second quarter of 2010. However, economic growth in the U.S. then moderated somewhat, as the Commerce Department reported that first quarter 2012 GDP growth was 1.9%.

Two factors constraining economic growth were the weak job market and continued troubles in the housing market. While there was some improvement during the reporting period, unemployment remained elevated. When the reporting period began, unemployment, as reported by the U.S. Department of Labor, was 9.0%. Unemployment stayed at or above 9.0% until October, when it dipped to 8.9%. Unemployment then declined during five out of the next six months and was 8.1% in April 2012, the lowest rate since January 2009. However, the unemployment rate then moved up to 8.2% in May 2012. The housing market showed some positive signs, although it still appears to be searching for a bottom. According to the National Association of Realtors (“NAR”), existing-home sales fluctuated throughout the period. Existing-home sales fell 1.5% on a seasonally adjusted basis in May 2012 versus the previous month. However, the NAR reported that the median existing-home price for all housing types was $182,600 in May 2012, up 7.9% from May 2011. In addition, the inventory of unsold homes fell 0.4% in May versus the previous month.

The manufacturing sector overcame a soft patch in the summer of 2011 and continued to expand during the reporting period. Looking back, based on the Institute for Supply Management’s PMI (“PMI”)ii, in February 2011, the manufacturing sector expanded at its fastest pace since May 2004, with a reading of 61.4 (a reading below 50 indicates a contraction, whereas a reading above 50 indicates an expansion). The PMI then generally moderated over the next several months and was 50.6 in August 2011, its lowest reading in two years. The manufacturing sector gathered momentum and ended January 2012 at 54.1, its highest reading since June 2011. The PMI then fluctuated over the last four months of the reporting period and was 53.5 in May 2012.

While the U.S. economy continued to expand during the reporting period, growth generally moderated overseas. In April 2012, the International Monetary Fund (“IMF”) stated that “global growth is projected to drop from about 4.0% in 2011 to about 3.5% in 2012 because of weak activity during the second half of 2011 and the first half of 2012.” The IMF now anticipates 2012 growth will be -0.3% in the Eurozone and 2.0% in Japan. While growth in emerging market countries is expected to remain higher than in their developed country counterparts, the IMF projects that growth will fall from approximately 5.8% in 2011 to 5.7% in 2012.

The Federal Reserve Board (“Fed”)iii took a number of actions as it sought to meet its dual mandate of fostering maximum employment and price stability.

Investment commentary (cont’d)

As has been the case since December 2008, the Fed kept the federal funds rateiv at a historically low range between zero and 0.25%. In August 2011, the Fed declared its intention to keep the federal funds rate steady until mid-2013. Then, in September 2011, the Fed announced its intention to purchase $400 billion of longer-term Treasury securities and to sell an equal amount of shorter-term Treasury securities by June 2012 (often referred to as “Operation Twist”). In January 2012, the Fed extended the period it expects to keep rates on hold, saying “economic conditions — including low rates of resource utilization and a subdued outlook for inflation over the medium run — are likely to warrant exceptionally low levels for the federal funds rate at least through late 2014.” In June, after the reporting period ended, the Fed announced that it would extend Operation Twist until the end of 2012 and that it was “prepared to take further action as appropriate to promote a stronger economic recovery and sustained improvement in labor market conditions in a context of price stability.”

Given the economic challenges in the Eurozone, the European Central Bank (“ECB”) lowered interest rates from 1.50% to 1.25% in November 2011. In December, the ECB lowered interest rates to 1.00%, equaling its all-time low. In other developed countries, the Bank of England kept rates on hold at 0.50% during the reporting period, as did Japan at a range of zero to 0.10%, the lowest level since 2006. With growth rates declining, both China and India lowered their cash reserve ratio for banks during the period. In June, after the reporting period ended, China lowered interest rates in an attempt to stimulate its economy.

As always, thank you for your confidence in our stewardship of your assets.

Sincerely,

R. Jay Gerken, CFA

Chairman, President and Chief Executive Officer

June 29, 2012

All investments are subject to risk including the possible loss of principal. Past performance is no guarantee of future results. Forecasts and predictions are inherently limited and should not be relied upon as an indication of actual or future performance.

i                Gross domestic product (“GDP”) is the market value of all final goods and services produced within a country in a given period of time.

ii             The Institute for Supply Management’s PMI is based on a survey of purchasing executives who buy the raw materials for manufacturing at more than 350 companies. It offers an early reading on the health of the manufacturing sector.

iii          The Federal Reserve Board (“Fed”) is responsible for the formulation of policies designed to promote economic growth, full employment, stable prices and a sustainable pattern of international trade and payments.

iv           The federal funds rate is the rate charged by one depository institution on an overnight sale of immediately available funds (balances at the Federal Reserve) to another depository institution; the rate may vary from depository institution to depository institution and from day to day.

Fund overview

Q. What is the Fund’s investment strategy?

A. The Fund’s primary investment objective is high current income and its secondary objective is total return. Under normal market conditions, the Fund invests in a global portfolio of securities consisting of below investment grade fixed-income securities, emerging market fixed-income securities and investment grade fixed-income securities. We have broad discretion to allocate the Fund’s assets among the following segments of the global market for below investment and investment grade fixed-income securities: corporate bonds, loans, preferred stock, mortgage- and asset-backed securities and sovereign debt, and derivative instruments of the foregoing securities. The Fund may use a variety of derivative instruments, such as options, futures contracts, swap agreements and credit default swaps, as part of its investment strategies or for hedging or risk management purposes.

At Western Asset Management Company (“Western Asset”), the Fund’s subadviser, we utilize a fixed-income team approach, with decisions derived from interaction among various investment management sector specialists. The sector teams are comprised of Western Asset’s senior portfolio managers, research analysts and an in-house economist. Under this team approach, management of client fixed-income portfolios will reflect a consensus of interdisciplinary views within the Western Asset organization. The portfolio managers responsible for development of investment strategy, day-to-day portfolio management, oversight and coordination of the Fund are S. Kenneth Leech, Stephen A. Walsh, Michael C. Buchanan, Keith J. Gardner and Ryan Brist.

Q. What were the overall market conditions during the Fund’s reporting period?

A. The spread sectors (non-Treasuries) experienced periods of volatility during the reporting period, but ultimately generated positive results. Risk aversion generally ruled the markets from June through September 2011, given mostly disappointing economic data, the European sovereign debt crisis and the Standard & Poor’s rating downgrade of U.S. sovereign debt. Most spread sectors then rallied in October given hopes of progress in Europe and some better-than-expected economic data. While risk aversion returned in November given an escalation of the European sovereign debt crisis, risk appetite returned in December and generally remained robust during the next three months. This shift in investor sentiment was triggered by indications that the U.S. economy was gathering momentum and signs of progress in the European sovereign debt crisis. However, fears that the economy may be experiencing a soft patch and contagion fears from Europe led to periods of heightened risk aversion late in the period.

Both short- and long-term Treasury yields moved lower during the reporting period. When the period began, two- and ten-year Treasury yields were 0.45% and 3.05%, respectively. Treasury yields initially moved higher and two- and ten-year Treasury yields peaked at 0.50% and 3.22%, respectively, on July 1, 2011. Yields then declined during much of the next two months due to disappointing economic data, and two-year Treasuries hit their low for the reporting period of 0.16% on September 19, 2011. Yields then moved higher during much of the next six months as the economy gained

Fund overview (cont’d)

some traction and rising oil prices fanned inflationary concerns. However, yields moved sharply lower in April and May given some moderating economic data in the U.S. and renewed fears regarding the situation in Europe. When the reporting period ended on May 31, 2012, two-year Treasury yields were 0.27% and ten-year Treasury yields were 1.59% – a record low.

The Barclays Capital U.S. Aggregate Indexi returned 7.12% for the twelve months ended May 31, 2012. Investment grade corporate bonds posted solid results, with the Barclays Capital U.S. Credit Indexii returning 8.28%. Comparatively, riskier fixed-income securities produced mixed results. Over the fiscal year, the Barclays Capital U.S. High Yield – 2% Issuer Cap Indexiii returned 3.97%. During this period, as measured by the Index, lower-quality CCC-rated bonds underperformed higher-quality BB-rated securities, returning 0.82% and 5.59%, respectively. In contrast, emerging market debt, as measured by the JPMorgan Emerging Markets Bond Index Global (“EMBI Global”)iv, returned 8.28% for the twelve months ended May 31, 2012. At the same time, corporations domiciled in emerging market countries lagged the performance of their sovereign counterparts, as the Barclays Emerging Market U.S. Dollar Corporate Indexv returned 2.60%.

Q. How did we respond to these changing market conditions?

A. A number of adjustments were made to the Fund’s portfolio during the reporting period. We increased the Fund’s overall credit quality by paring its allocation to high-yield bonds and increasing its exposure to investment grade corporate bonds. In particular, we added to the Fund’s allocation in the Financials sector. Additionally, we actively participated in the new issuance market by selectively purchasing securities that we felt were attractively valued.

Currency forwards were used to hedge the Fund’s currency risk and manage our non-U.S. dollar currency exposures. They were positive for performance, primarily due to the success of hedging our exposure to the euro. The Fund employed U.S. Treasury futures to manage its yield curvevi positioning and durationvii, which was a small detractor. We utilized index credit default swaps and options on index credit default swaps to reduce the Fund’s exposure to the high-yield market in the event of a pullback. This strategy was a contributor to performance given the high-yield market’s weakness at times during the reporting period. Finally, credit default swaps, which were used to manage the Fund’s Brazilian exposure, did not meaningfully impact performance. All told, the net impact from the use of derivatives was positive during the twelve months ended May 31, 2012.

During the reporting period, we tactically utilized leverage in the Fund. We ended the period with leverage as a percentage of gross assets, of approximately 22.2%. This represented a modest increase during the fiscal year. The use of leverage was additive for results given the positive performance of emerging market debt, investment grade corporate bonds and high-yield bonds.

Performance review

For the twelve months ended May 31, 2012, Western Asset Global High Income Fund Inc. returned 2.81%

based on its net asset value (“NAV”)viii and 5.32% based on its New York Stock Exchange (“NYSE”) market price per share. The Fund’s unmanaged benchmarks, the Barclays Capital U.S. Aggregate Index, the Barclays Capital U.S. High Yield – 2% Issuer Cap Index and the EMBI Global, returned 7.12%, 3.97% and 8.28%, respectively, for the same period. The Lipper High Current Yield (Leveraged) Closed-End Funds Category Averageix returned 3.79% over the same time frame. Please note that Lipper performance returns are based on each fund’s NAV.

During the twelve-month period, the Fund made distributions to shareholders totaling $1.16 per share. The performance table shows the Fund’s twelve-month total return based on its NAV and market price as of May 31, 2012. Past performance is no guarantee of future results.

Performance Snapshot as of May 31, 2012

All figures represent past performance and are not a guarantee of future results.

*       Total returns are based on changes in NAV or market price, respectively.

†        Total return assumes the reinvestment of all distributions at NAV.

‡       Total return assumes the reinvestment of all distributions in additional shares in accordance with the Fund’s Dividend Reinvestment Plan.

Q. What were the leading contributors to performance?

A. The portfolio’s exposure to the investment grade corporate bond market was the largest contributor to the Fund’s absolute performance during the reporting period. In particular, our allocations to American International Group Inc. and its aircraft leasing arm International Lease Finance Corp. and General Electric Capital Corp. (“GE Capital”) contributed to performance. American International Group Inc.’s senior debt performed well as the company continued to reduce its debt levels and recapitalize its business. Management also remained focused on its fundamentals, which improved over the period. International Lease Finance Corp. continued to access the capital markets and extend its maturity profile. Prudent balance sheet management, along with improving fundamental results, caused the issuer’s bonds to perform well during the period. GE Capital is the financial services unit of General Electric. It provides commercial lending and leasing, as well as a range of financial services for businesses around the world. GE Capital’s bonds performed well during the reporting period, along with the overall Financials sector. General Electric reported its eighth consecutive quarter of strong earnings growth during the first quarter of 2012, driven by strong infrastructure, equipment and services orders. Additionally, organic industrial growth was impressive as orders increased by more than 14% during the reporting period. Investors were encouraged by these positive readings and GE Capital’s bonds reacted positively.

The Fund’s emerging market debt exposure also contributed to performance. In particular, the Fund’s Venezuelan sovereign debt generated strong results. Economic growth in the country remained solid and our holdings generally offered attractive, double-digit yields. Our allocation to Peru

Fund overview (cont’d)

was also rewarded. This higher quality Latin American country performed well based on continued solid economic performance in terms of Gross Domestic Product (“GDP”)x growth, low deficits and a strong liquidity position. Elsewhere, the Fund’s position in Petroleos Mexicanos, a Mexican state owned integrated petroleum company, performed well. The company benefited from its monopoly status in Mexico and its rank as a top crude oil exporter to the U.S.

Our exposure to several high-yield bonds was also additive for performance during the reporting period. Examples of holdings that contributed to performance were Charter Communications (Charter Communications Inc., CCO Holdings LLC, and CCH II LLC), Intelsat (Intelsat Jackson Holdings Ltd. and Intelsat Luxembourg S.A.) and El Pollo Loco Inc. Charter Communications, an operator of cable television systems in the U.S., offers a full range of traditional and digital cable television services. We felt the market was not valuing Charter Communications’ business appropriately given our expectations for strong growth in its small and medium enterprises segment, as well as its retail data businesses. Our holding in Charter Communications was rewarded, as the company posted solid fundamental results and improving free cash flow during the period. Intelsat is a global satellite communications services provider which produced solid fundamental results during the reporting period. We added Intelsat Luxembourg S.A subordinated debt when the high-yield market sold off during the third quarter of 2011. This was beneficial as its debt rallied more than the market later in the reporting period. El Pollo Loco is a fast food restaurant chain specializing in Mexican grilled chicken. During the reporting period, we exchanged our existing El Pollo Loco bonds into a longer maturity, higher coupon bond issued by the company to help extend our maturity profile and reduce liquidity concerns. The bonds have outperformed as the company has since posted improved fundamental results, driven by an overhaul of its menu as well as its successful promotional activities.

Q. What were the leading detractors from performance?

A. While the portfolio’s exposure to the high-yield market added to returns on an absolute basis, our positioning within our high-yield allocation detracted from results relative to the peer group. Specifically an emphasis on lower quality high-yield bonds and the Fund’s exposure to European high-yield issuers were not rewarded. The market discounted the generally strong fundamental corporate credit backdrop and improved high-yield balance sheets in favor of more interest rate sensitive lower risk credits. While our positioning has benefited the portfolio in 2012, the Fund would have been better served favoring higher quality high-yield, investment grade corporate bonds and emerging market sovereigns during the period.

In terms of individual holdings, Petroplus Finance Ltd. and CMA CGM detracted from performance. Petroplus Finance is a European oil refiner. In December 2011, a $1 billion credit line to the company was frozen by its bank lenders. The company entered into negotiations to restore the credit line to avoid bankruptcy and it reduced its output and closed several refineries.

The negotiations failed and, in January 2012, Petroplus announced that it was filing for insolvency after it defaulted on $1.75 billion of senior notes and convertible bonds. CMA CGM, based in France, is the world’s third largest container shipping company. The firm performed poorly due to a variety of factors, including signs that global economic growth was decelerating, higher oil prices, accelerated capacity additions and fears related to the escalating European sovereign debt crisis. CMA CGM bonds did recover during the second half of the reporting period but were a net negative contributor to absolute performance.

The Fund’s allocation to Argentinean emerging market debt was detrimental to performance. Influenced greatly by political concerns, performance was hurt as negative investor sentiment for Argentinean debt peaked during the reporting period. Our exposure to Axtel was also a drag on the Fund’s results. Axtel is Mexico’s second largest fixed line, integrated telecommunication company, with services in local and long distance telephone, Internet, data and consulting services. Axtel bonds were negatively impacted by the decline in the Mexican peso, which weakened its credit metrics due to the relative increase in the value of the company’s U.S. dollar denominated liabilities. Its bonds were also impacted by the competitive telecommunication landscape and a volatile market environment which led to a general sell-off in many lower rated bonds.

Finally, in the investment grade corporate bond market, having a position in Credit Agricole, the largest retail bank in France, detracted from results. It performed poorly given the ongoing European sovereign debt crisis and fears of contagion from peripheral Eurozone countries, such as Greece, to core Eurozone countries, including France. Additionally, Credit Agricole was penalized for its direct exposure to the Greek banking system through its majority owned subsidiary, Emporiki Bank.

Looking for additional information?

The Fund is traded under the symbol “EHI” and its closing market price is available in most newspapers under the NYSE listings. The daily NAV is available on-line under the symbol “XEHIX” on most financial websites. Barron’s and the Wall Street Journal’s Monday edition both carry closed-end fund tables that provide additional information. In addition, the Fund issues a quarterly press release that can be found on most major financial websites as well as www.lmcef.com.

In a continuing effort to provide information concerning the Fund, shareholders may call 1-888-777-0102 (toll free), Monday through Friday from 8:00 a.m. to 5:30 p.m. Eastern Time, for the Fund’s current NAV, market price and other information.

Thank you for your investment in Western Asset Global High Income Fund Inc. As always, we appreciate that you have chosen us to manage

Fund overview (cont’d)

your assets and we remain focused on achieving the Fund’s investment goals.

Sincerely,

Western Asset Management Company

June 19, 2012

RISKS: Fixed-income securities are subject to credit risk, inflation risk, call risk and interest rate risk. An investment in the Fund is subject to investment risk, including the possible loss of the entire principal amount that you invest. As interest rates rise, bond prices fall, reducing the value of the Fund’s holdings. The Fund may use derivatives, such as options, futures contracts, swap agreements and credit default swaps, which can be illiquid, may disproportionately increase losses and have a potentially large impact on Fund performance. Investing in foreign securities is subject to certain risks not associated with domestic investing, such as currency fluctuations, and changes in political, regulatory and economic conditions. These risks are magnified in emerging or developing markets. High-yield bonds involve greater credit risk (risk of default) and liquidity risk than investment grade bonds. Leverage may magnify gains and increase losses in the Fund’s portfolio.

Portfolio holdings and breakdowns are as of May 31, 2012 and are subject to change and may not be representative of the portfolio managers’ current or future investments. Please refer to pages 11 through 33 for a list and percentage breakdown of the Fund’s holdings.

The mention of sector breakdowns is for informational purposes only and should not be construed as a recommendation to purchase or sell any securities. The information provided regarding such sectors is not a sufficient basis upon which to make an investment decision. Investors seeking financial advice regarding the appropriateness of investing in any securities or investment strategies discussed should consult their financial professional. The Fund’s top five sector holdings (as a percentage of net assets) as of May 31, 2012 were: Sovereign Bonds (24.7%), Consumer Discretionary (19.2%), Energy (18.3%), Financials (13.8%) and Industrials (11.8%). The Fund’s portfolio composition is subject to change at any time.

All investments are subject to risk including the possible loss of principal. Past performance is no guarantee of future results. All index performance reflects no deduction for fees, expenses or taxes. Please note that an investor cannot invest directly in an index.

The information provided is not intended to be a forecast of future events, a guarantee of future results or investment advice. Views expressed may differ from those of the firm as a whole.

i                The Barclays Capital U.S. Aggregate Index is a broad-based bond index comprised of government, corporate, mortgage- and asset-backed issues, rated investment grade or higher, and having at least one year to maturity.

ii             The Barclays Capital U.S. Credit Index is an index composed of corporate and non-corporate debt issues that are investment grade (rated Baa3/BBB- or higher).

iii          The Barclays Capital U.S. High Yield — 2% Issuer Cap Index is an index of the 2% Issuer Cap component of the Barclays Capital U.S. Corporate High Yield Index, which covers the U.S. dollar-denominated, non-investment grade, fixed-rate, taxable corporate bond market.

iv           The JPMorgan Emerging Markets Bond Index Global (“EMBI Global”) tracks total returns for U.S. dollar-denominated debt instruments issued by emerging market sovereign and quasi-sovereign entities: Brady bonds, loans, Eurobonds and local market instruments.

v              The Barclays Emerging Market U.S. Dollar Corporate Index is a subset of the Barclays U.S. Emerging Markets Index, which includes fixed- and floating-rate U.S. dollar-denominated debt from emerging markets in the following regions: Americas, Europe, Middle East, Africa, and Asia.

vi           The yield curve is the graphical depiction of the relationship between the yield on bonds of the same credit quality but different maturities.

vii        Duration is the measure of the price sensitivity of a fixed-income security to an interest rate change of 100 basis points. Calculation is based on the weighted average of the present values for all cash flows.

viii     Net asset value (“NAV”) is calculated by subtracting total liabilities and outstanding preferred stock (if any) from the closing value of all securities held by the Fund (plus all other assets) and dividing the result (total net assets) by the total number of the common shares outstanding. The NAV fluctuates with changes in the market prices of securities in which the Fund has invested. However, the price at which an investor may buy or sell shares of the Fund is the Fund’s market price as determined by supply of and demand for the Fund’s shares.

ix            Lipper, Inc., a wholly-owned subsidiary of Reuters, provides independent insight on global collective investments. Returns are based on the twelve-month period ended May 31, 2012, including the reinvestment of all distributions, including returns of capital, if any, calculated among the 39 funds in the Fund’s Lipper category.

x               Gross domestic product (“GDP”) is the market value of all final goods and services produced within a country in a given period of time.

Fund at a glance† (unaudited)

Investment breakdown (%) as a percent of total investments

Spread duration (unaudited)

Economic Exposure — May 31, 2012

Spread duration measures the sensitivity to changes in spreads. The spread over Treasuries is the annual risk-premium demanded by investors to hold non-Treasury securities. Spread duration is quantified as the % change in price resulting from a 100 basis points change in spreads. For a security with positive spread duration, an increase in spreads would result in a price decline and a decline in spreads would result in a price increase. This chart highlights the market sector exposure of the Fund’s sectors relative to the selected benchmark sectors as of the end of the reporting period.

Effective duration (unaudited)

Interest Rate Exposure — May 31, 2012

Effective duration measures the sensitivity to changes in relevant interest rates. Effective duration is quantified as the % change in price resulting from a 100 basis points change in interest rates. For a security with positive effective duration, an increase in interest rates would result in a price decline and a decline in interest rates would result in a price increase. This chart highlights the interest rate exposure of the Fund’s sectors relative to the selected benchmark sectors as of the end of the reporting period.

Schedule of investments

May 31, 2012

Western Asset Global High Income Fund Inc.

See Notes to Financial Statements.

Schedule of investments (cont’d)

May 31, 2012

Western Asset Global High Income Fund Inc.

See Notes to Financial Statements.

Western Asset Global High Income Fund Inc.

See Notes to Financial Statements.

Schedule of investments (cont’d)

May 31, 2012

Western Asset Global High Income Fund Inc.

See Notes to Financial Statements.

Western Asset Global High Income Fund Inc.

See Notes to Financial Statements.

Schedule of investments (cont’d)

May 31, 2012

Western Asset Global High Income Fund Inc.