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 Phillips Edison Grocery Center REIT III, Inc. (the “Registrant”) for the six months ended June 30, 2019, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), the undersigned, Jeffrey S. Edison, Chief Executive Officer of the Registrant, hereby certifies, pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, that, to the best of his knowledge and belief:

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 Registrant.

Date: August 8, 2019

/s/ Jeffrey S. Edison

Jeffrey S. Edison

Chairman of the Board and Chief Executive Officer

(Principal Executive Officer)