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

In connection with the Quarterly Report on Form 10-Q of Golub Capital BDC, Inc. (the “Company”), for the quarterly period ended December 31, 2020, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), we, David B. Golub and Ross A. Teune, Chief Executive Officer and Chief Financial Officer, respectively, of the Company, certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that to our knowledge:

(1) The Report fully complies with the requirements of section 13(a) or 15(d) of the Securities Exchange
Act of 1934; and

(2) The information contained in the Report fairly presents, in all material respects, the financial condition
and results of operations of the Company.

Date: February 8, 2021	/s/ David B. Golub
	David B. Golub Chief Executive Officer
	/s/ Ross A. Teune
	Ross A. Teune Chief Financial Officer