Exhibit 32.1

CERTIFICATION PURSUANT TO 18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

The undersigned, the Chief Executive Officer and Chairman of the Board of Gladstone Capital Corporation (the “Company”), hereby certifies on the date hereof, pursuant to 18 U.S.C. §1350(a), as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that the Quarterly Report on Form 10-Q for the quarter ended June 30, 2014 (“Form 10-Q”), filed concurrently herewith by the Company, fully complies with the requirements of Section 13(a) or Section 15(d) of the Securities Exchange Act of 1934, as amended, and that the information contained in the Form 10-Q fairly presents, in all material respects, the financial condition and results of operations of the Company.

Dated: July 30, 2014