Goldman Sachs Private Middle Market Credit 10-K 2018 FY Annual report

Exhibit 32.1

Certification of Chief Executive Officer and Chief Financial Officer

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 Annual Report on Form10-K of Goldman Sachs Private Middle Market Credit LLC (the “Company”) for the annual period ended December 31, 2018 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), Brendan McGovern, as Chief Executive Officer of the Company, and Jonathan Lamm, 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 the best of his knowledge:

1. The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; 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 28, 2019

/s/ Brendan McGovern

Brendan McGovern

Chief Executive Officer

(Principal Executive Officer)

Date: February 28, 2019

/s/ Jonathan Lamm

Jonathan Lamm

Chief Financial Officer and Treasurer

(Principal Financial Officer)