SCHEDULE 14A

Proxy Statement Pursuant to Section 14(a)

of the Securities Exchange Act of 1934

Filed by the Registrant ¨

Filed by a Party other than the Registrant þ

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¨ Preliminary Proxy Statement

¨ Confidential, for Use of the Commission Only (as permitted by Rule 14a-6(e)(2))

¨ Definitive Proxy Statement

þ Definitive Additional Materials

¨ Soliciting Material Under Rule 14a-12

Western Asset Global High Income Fund Inc.

(Name of Registrant as Specified In Its Charter)

Saba Capital Management, L.P.

Saba Capital Master Fund, Ltd.

Saba Capital Master Fund II, Ltd.

Saba Capital CEF Opportunities 1, Ltd.

Saba Capital CEF Opportunities 2, Ltd.

Saba Capital Special Opportunities Fund, Ltd.

Boaz R. Weinstein

David Basile

Frederic Gabriel

(Name of Person(s) Filing Proxy Statement, if other than the Registrant)

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Dear Fellow Shareholders:

The purpose of this letter is to inform you about our proxy campaign with Western Asset Global High Income Fund Inc. (“EHI” or the “Fund”). Over the next few months you will receive numerous letters and phone calls orchestrated by the Fund’s investment advisors (Legg Mason and Western Asset Management) — a campaign to deceive you with false and misleading information. The Fund will charge the cost of this campaign to you as “fund expenses”.

We want to take the opportunity, before all of that starts, to set the record straight. We own approximately 7.8 million shares (17.8%) of the Fund. We are focused on fighting for the rights of shareholders and increasing the value of your investment by holding the advisers and the board of directors of the Fund (the “Board”) accountable for their poor decisions.

Worst in Class Performance

Each year, the Board is required by law to review and, if it finds the advisor’s performance acceptable, reapprove the advisory agreement between the Fund and the advisor. According to the Fund’s Annual Report, filed on July 29, 2019 (the “Annual Report”), in order to assist the Board in its review, the Board hired Broadridge Financial Solutions, Inc. (“Broadridge”), an independent third party, to evaluate the performance of the Fund, as well as a group of similarly situated funds.

Broadridge concluded that the Fund ranked in the lowest category for each of the 1-, 3- and 5- year performance periods. This means the Fund was one of the worst performing funds among its peer group.

Making matters worse, the Fund’s third largest position is an Argentina government bond. As the fear of an Argentina default looms, this bond lost 50% of its value in August alone!

Persistently High Discount

Despite what you may hear from Legg Mason and Western Asset Management, the Fund traded at an average discount to net asset value of -12.9% in 2018. This discount means that when your holdings are worth $100, you can only sell them for $87.1. Sadly, the Fund has traded at a discount for each of the last 75 months and counting! To the detriment of all shareholders, Legg Mason and Western Asset Management have either ignored the discount or been ineffective in addressing it.

Since Saba began buying the Fund’s shares, the Fund’s discount has narrowed sharply to -8%, to the benefit of all shareholders. We believe this signifies that shareholders are expecting Saba to be successful in bringing about change to the Fund. If Saba is not successful, we believe the discount will revert into the double digits, causing a loss for you.

High Fees Earned through Increased Investor Risk

According to the Annual Report, the Fund’s total expense ratio is 2.54%. A significant portion of this expense comes from high management fees and operating expenses.

One reason Legg Mason and Western Asset Management are able to extract such high management fees from your investment comes from a feature in their advisory agreement allowing them to charge management fees on daily net assets “plus the proceeds of any outstanding borrowings”. Instead of charging you fees based on the market value of the Fund, they are charging 61% more in fees. This scheme has clearly misaligned incentives between shareholders and management, and, we believe, incents Legg Mason and Western Asset Management to run a high level of leverage (since high leverage increases their fees) in this portfolio of already risky bonds.

We need your support to hold the advisor and the Board accountable.

PLEASE VOTE FOR THE ELECTION OF SABA’S NOMIEES (PROPOSAL 1) AND FOR THE PROPOSAL TO DECLASSIFY THE BOARD (PROPOSAL 2).

If you have already returned Management’s white proxy card, you can still support Saba by returning the enclosed GOLD proxy card. Only your latest dated proxy card submission will count.

Sincerely,

Saba Capital Management, L.P.

212-542-4646

Legend

Saba Capital Management, L.P. (“Saba Capital”), Saba Capital Master Fund, Ltd., Saba Capital Master Fund II, Ltd., Saba Capital CEF Opportunities 1, Ltd., Saba Capital CEF Opportunities 2, Ltd., Saba Capital Special Opportunities Fund, Ltd., a separately managed account managed by Saba Capital, Boaz R. Weinstein, David Basile and Frederic Gabriel (collectively, the “Participants”) have filed with the Securities and Exchange Commission (the “SEC”) a definitive proxy statement and accompanying form of proxy to be used in connection with the solicitation of proxies from the shareholders of Western Asset Global High Income Fund Inc. (the “Fund”). All shareholders of the Fund are advised to read the definitive proxy statement and other documents related to the solicitation of proxies by the Participants, as they contain important information, including additional information related to the Participants. The definitive proxy statement and an accompanying proxy card has been furnished to some or all of the Fund’s shareholders and is, along with other relevant documents, available at no charge on the SEC website at http://www.sec.gov/.

Information about the Participants and a description of their direct or indirect interests by security holdings is contained in the definitive proxy statement on Schedule 14A filed by Saba Capital with the SEC on September 6, 2019.