UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

WASHINGTON, D.C. 20549

SCHEDULE 14A

Proxy Statement Pursuant to Section 14(a) of the

Securities Exchange Act of 1934

(Amendment No.    )

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Nuveen Global High Income Fund (JGH)
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Nuveen Global High Income Fund Sends Letter to Shareholders

The Fund Has Delivered Competitive Long-Term Returns and High Current Income to Shareholders, Executing on Its Stated Investment Objective

The Fund’s Current Board of Trustees Has an Extensive Track Record of Enhancing Long-Term Shareholder Value

Vote on the WHITE Proxy Card Today “FOR ALL” the Fund’s Experienced Nominees

CHICAGO – February 12, 2021 – Nuveen Global High Income Fund (NYSE: JGH) today announced that it will mail a letter to shareholders along with its proxy statement in connection with the Fund’s upcoming Annual Meeting of Shareholders to be held on April 6, 2021. The full text of the letter to be sent on February 12, 2021, is below.

February 12, 2021

Dear Shareholder,

This year’s Annual Meeting for Nuveen Global High Income Fund, to be held on April 6, 2021, is crucial to determine the future of your Fund. Your vote will have a significant impact on your investment, as you will have an important choice to make, deciding between:

• Supporting your Board’s highly qualified nominees—Jack B. Evans, Albin F. Moschner and Matthew Thornton III—whose collective closed-end fund experience contributes to the Board’s efforts to serve the interests of long-term shareholders; or

• Voting for a proposal from a short-term focused hedge fund, Saba Capital Master Fund, Ltd., to pack the Board with its hand-picked nominees who lack any relevant closed-end fund experience and are beholden to the short-term interests of Saba.

In making this important decision, we would encourage you to consider the following. Your Fund, under the supervision of its current Board, has delivered for investors with strong long-term performance:

• The Fund has fulfilled its stated investment objective of providing high current income by paying a meaningfully higher distribution yield than its benchmark (the Bloomberg Barclays Global High Yield Hedged Index) over the trailing 3-year, 5-year and since inception periods.

• The Fund has provided compelling long-term returns, with a 5-year annualized return of 10.47% on net asset value (“NAV”) and 13.15% on market price, outperforming its peers and its benchmark as of 1/31/2021.

Your Fund’s Board is composed of highly qualified, experienced Trustees currently overseeing 67 Nuveen closed-end funds. This direct experience with closed-end funds provides the Trustees with unique viewpoints and insights, enabling a strong, consistent and effective governance structure. This includes a history of actions designed to enhance shareholder value. Particular strengths of your Fund’s Board include the following:

• The Board has a diverse set of Trustees with unique qualifications, including deep experience across product types, asset classes, investment strategies and market cycles. This stands in stark contrast to the Saba hedge fund’s proposed nominees who lack any relevant closed-end fund experience.

• The Board has engaged in frequent market trading reviews resulting in actions designed to address discounts, including multi-year complex-wide share repurchases and numerous fund mergers.

• The Board designed and implemented an innovative complex-wide breakpoint fee schedule that lowers fees for all shareholders as Nuveen fund assets grow. Breakpoint pricing currently provides shareholders across the Nuveen fund complex annualized savings of approximately $26.7 million per year.

We urge you to review the enclosed proxy materials, which outline why we believe your Board’s nominees deserve your vote. Voting takes just a few minutes and can be done online, by phone or mail by following the instructions on the WHITE proxy card.

The addition of the Saba hedge fund’s hand-picked nominees could disrupt your Board’s efforts to enhance long-term shareholder value. If elected, Saba’s hand-picked nominees will likely seek to take actions that would advance Saba’s near-term interests at the expense of long-term investors who rely on this Fund for competitive returns and consistent, high current income. Don’t let a self-interested hedge fund like Saba put your investment and your opportunity for future returns at risk. You can reject their efforts by voting your WHITE proxy card “FOR ALL” of your Board’s experienced and qualified nominees.

The Saba hedge fund may contact you by mail to solicit your vote. Please do not mail in the proxy card sent to you by the Saba hedge fund or any proxy card other than the WHITE proxy card, as doing so would cancel your vote to support your Fund and its current Board.

Thank you for your continued support.

Sincerely,

Terence J. Toth

Chair of the Board of Trustees

Nuveen Global High Income Fund

If you have any questions, please call the Fund’s proxy solicitor, Georgeson LLC, toll-free at 866-431-2108.