Amendment No. 1 to Equity Distribution Agreement, dated as of August 5, 2022, by and among Gladstone Capital Corporation, Gladstone Management Corporation, Gladstone Administration, LLC and Jefferies LLC, as the sales agent

Exhibit 1.1

AMENDMENT NO. 1 TO THE EQUITY DISTRIBUTION AGREEMENT

August 5, 2022

JEFFERIES LLC

520 Madison Avenue

New York, New York 10022

Ladies and Gentlemen:

This Amendment No. 1 to the Equity Distribution Agreement (this “Amendment”) is entered into as of the date first written above by and among Gladstone Capital Corporation, a corporation organized under the laws of Maryland (the “Company”), Gladstone Management Corporation, a Delaware corporation registered as an investment adviser (the “Adviser”), Gladstone Administration, LLC, a Delaware limited liability company (the “Administrator”), and Jefferies LLC (“Agent”), that are parties to that certain Equity Distribution Agreement, dated May 10, 2021 (the “Original Agreement”). All capitalized terms not defined herein shall have the meanings ascribed to them in the Original Agreement. The parties, intending to be legally bound, hereby amend the Original Agreement as follows:

1. The second paragraph of Section 1 to the Original Agreement is hereby deleted in its entirety and replaced with the following:

“The Company has entered into a fourth amended and restated investment advisory and management agreement, dated as of April 12, 2022 (the “Investment Advisory Agreement”), with the Adviser. The Company has entered into an administration agreement, dated as of October 1, 2006 (the “Administration Agreement”), with the Administrator.”

2. The third paragraph of Section 1 to the Original Agreement is hereby deleted in its entirety and replaced with the following:

“The Company has filed, pursuant to the 1933 Act, with the Commission a registration statement on Form N-2 (File No. 333-261398), which registers the offer and sale of certain securities to be issued from time to time by the Company, including the Shares.”

3. The fourth paragraph of Section 1 to the Original Agreement is hereby amended by adding the following after the first sentence thereof:

“The Company may file one or more registration statements after the date hereof which may be referred to as the Registration Statement, only to the extent that such registration statement relates to the Common Stock offered and sold pursuant to this Agreement.”

4. Any references in the Original Agreement to “Proskauer Rose LLP,” as counsel to the Company, the Adviser and the Administrator shall be replaced with “Kirkland & Ellis LLP”.

5. Section 11 to the Original Agreement is hereby deleted in its entirety and replaced with the following:

“Notices. All communications hereunder will be in writing and effective only on receipt, and, if sent to the Agent, will be mailed, delivered or telefaxed to (i) Jefferies LLC, at 520 Madison Avenue, New York, NY 10022, fax no. (646) 786-5719, Attention: General Counsel, respectively, and Cooley LLP, 55 Hudson Yards, New York, NY 10001, fax. no ###-###-####, Attention: Daniel I. Goldberg; or (ii) if sent to the Company, the Adviser or the Administrator, will be mailed, delivered or telefaxed to it at ###-###-#### and confirmed to it at Gladstone Capital Corporation, 1521 Westbranch Drive, Suite 100, McLean, VA 22102, Attention: David Gladstone, with a copy to William J. Tuttle, Kirkland & Ellis LLP, 1301 Pennsylvania Ave, N.W., Washington, D.C. 20004, fax. No. (202) 389 5200 (which copy shall not constitute notice).”

6. The Company, the Adviser and the Administrator, jointly and severally, represents and warrants to, and agrees with the Agent that: this Amendment has been duly authorized, executed and delivered by, and is a valid and binding agreement of, the Company, the Adviser and the Administrator, enforceable in accordance with its terms, except as rights to indemnification hereunder may be limited by applicable law and except as the enforcement hereof may be limited by bankruptcy, insolvency, reorganization, moratorium or other similar laws relating to or affecting the rights and remedies of creditors or by general equitable principles.

7. Except as expressly amended by this Amendment, the Original Agreement remains in full force and effect. Neither this Amendment nor any term hereof may be amended except pursuant to a written instrument executed by the Company, the Adviser and the Administrator and the Agent. In the event that any one or more of the provisions contained herein, or the application thereof in any circumstance, is held invalid, illegal or unenforceable as written by a court of competent jurisdiction, then such provision shall be given full force and effect to the fullest possible extent that it is valid, legal and enforceable, and the remainder of the terms and provisions herein shall be construed as if such invalid, illegal or unenforceable term or provision was not contained herein, but only to the extent that giving effect to such provision and the remainder of the terms and provisions hereof shall be in accordance with the intent of the parties as reflected in this Amendment. All references in the Original Agreement to the “Agreement” shall mean the Original Agreement as amended by this Amendment; provided, however, that all references to “date of this Agreement” in the Original Agreement shall continue to refer to the date of the Original Agreement.

8. This Amendment shall be governed by and construed in accordance with the laws of the State of New York applicable to contracts made and to be performed within the State of New York. Each party hereby irrevocably submits to the non-exclusive jurisdiction of the state and federal courts sitting in the City of New York, Borough of Manhattan, for the adjudication of any dispute hereunder or in connection with any transaction contemplated hereby, and hereby irrevocably waives, and agrees not to assert in any suit, action or proceeding, any claim that it is not personally subject to the jurisdiction of any such court, that such suit, action or proceeding is

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brought in an inconvenient forum or that the venue of such suit, action or proceeding is improper. Each party hereby irrevocably waives personal service of process and consents to process being served in any such suit, action or proceeding by mailing a copy thereof (certified or registered mail, return receipt requested) to such party at the address in effect for notices to it under the Original Agreement and this Amendment and agrees that such service shall constitute good and sufficient service of process and notice thereof. Nothing contained herein shall be deemed to limit in any way any right to serve process in any manner permitted by law. The provisions of this paragraph shall survive any termination of this Amendment.

9. This Amendment may be executed in two or more counterparts, each of which shall be deemed an original, but all of which together shall constitute one and the same instrument. Delivery of an executed amendment by one party to the other may be made by facsimile transmission or by electronic delivery of a portable document format (PDF) file (including any electronic signature covered by the U.S. federal ESIGN Act of 2000, Uniform Electronic Transactions Act, the Electronic Signatures and Records Act or other applicable law, e.g., www.docusign.com).

[Remainder of Page Intentionally Blank]

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If the foregoing correctly sets forth your understanding of our agreement, please so indicate in the space provided below for that purpose, whereupon this letter shall constitute a binding amendment to the Original Agreement by and among the Company, the Adviser, the Administrator and the Agent.

[Signature Page to Amendment No. 1 to the Sales Agreement]