SCHEDULE 14A

(Rule 14a-101)

INFORMATION REQUIRED IN PROXY STATEMENT

SCHEDULE 14A INFORMATION

Proxy Statement Pursuant to Section 14(a) of the

Securities Exchange Act of 1934

(Amendment No.     )

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WESTERN ASSET GLOBAL HIGH INCOME FUND INC.

(Name of Registrant as Specified in Its Charter)

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September 17, 2019

Dear Fellow Stockholder:

The Western Asset Global High Income Fund Board has a strong track record of working with the Fund’s management team to deliver significant returns¹ that outpace our peer group averages. The Board is independent, diverse, and has the right financial expertise and other relevant skills to continue to act in your best interests and build on this positive momentum. We urge you to vote “FOR” the Board Nominees and “AGAINST” Saba Capital’s Board De-Classification Proposal on the WHITE Proxy Card today to protect the value of your investment.

The Board Has Increased Distributions to Deliver More Capital to Stockholders

We know stockholders invest in the Fund for our stable distribution payouts. We are focused on continuing to meet and exceed your expectations.

Under the Board’s Oversight, We Have Outperformed Peer Groups and Benchmarks Over Key Timeframes

The Board’s work with the Fund’s management team has not only increased distributions, but has led to total returns that consistently outpace our Lipper peer group² and key benchmark⁴ averages over the last decade.

Saba Capital is Waging a Campaign of Misinformation

Saba Capital, a professional activist hedge fund, has launched a proxy contest against the Fund in an attempt to facilitate its short-term strategy to the potential detriment of all of our long-term stockholders. In its communications to stockholders, Saba Capital is citing outdated and cherry picked performance metrics in an attempt to deceive stockholders into supporting its position. For example, the hedge fund is using 2018 data to highlight the Fund’s discount to NAV, but ignoring that the Fund has taken steps that have significantly reduced its discount to NAV over the course of 2019. This is the same playbook Saba Capital has used in its campaigns against numerous other closed-end funds over the last several years. We are committed to defending the Fund against this attack and preventing Saba Capital from executing its self-interested agenda at your expense.

Protect the Value of Your Investment by Voting the WHITE Proxy Card Today

Let your voice be heard. We urge you to vote “FOR” the Board Nominees and “AGAINST” Saba Capital’s Board De-Classification Proposal today by telephone, internet or by signing, dating and returning the enclosed WHITE Proxy card in the postage-paid envelope provided.

We appreciate your support during this critical moment in the Fund’s history.

Sincerely,

The Western Asset Global High Income Fund Inc.

Board of Directors

Notes

1 The Fund’s performance is based on the price of the Fund’s securities, which are listed for trading on the NYSE.

2 The Fund’s Lipper peer group refers to the peer group of high-yield, levered closed-end funds as selected by Lipper, an independent nationally recognized provider of investment company information.

3 Yield based on market price as of June 30, 2019.

4 The benchmark is based on a blend, in equal parts, of the Bloomberg Barclays U.S. Corporate High Yield — 2% Issuer Cap Index, the Bloomberg Barclays U.S. Aggregate Index, and the JPMorgan Emerging Markets Bond Index Global (EMBI Global). Additional information about the indexes can be found in the Fund’s annual shareholder report. Additional information about the Fund’s performance and about the history of the Board and the Fund’s management generating strong investor returns is included in the Fund’s Proxy Statement and in the Fund’s annual shareholder report.

Forward Looking Statement

Past performance is no guarantee of future results. The information provided is not intended to be a forecast of future events, a guarantee of future results or investment advice.

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