FS Investment Corp III 10-Q 2017 Q1 Quarterly report

Exhibit 32.1

CERTIFICATION OF CEO AND CFO 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 Form10-Q of FS Investment Corporation III (the “Company”) for the three months ended March 31, 2017, as filed with the Securities and Exchange Commission on the date hereof (the“Form 10-Q”), Michael C. Forman, as Chief Executive Officer of the Company, and Edward T. Gallivan, Jr., as Chief Financial Officer of the Company, each hereby certifies, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that, to my knowledge:

• theForm 10-Q of the Company fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934 (15 U.S.C. 78m or 78o(d)); and

• the information contained in theForm 10-Q fairly presents, in all material respects, the financial condition and results of operations of the Company.

Dated: May 11, 2017

/S/ MICHAEL C. FORMAN

Michael C. Forman

Chief Executive Officer

/S/ EDWARD T. GALLIVAN, JR.

Edward T. Gallivan, Jr.

Chief Financial Officer