Martin Midstream Partners (MMLP) 10-K 2015 FY Annual report

Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

The Board of Directors

Martin Midstream GP LLC:

We consent to the incorporation by reference in the registration statements on Form S-3 (No. 333-198514 and No. 333-193715) and on Form S-8 (No. 333-203857 and No. 333-140152) of Martin Midstream Partners L.P. of our reports dated February 29, 2016, with respect to the consolidated balance sheets of Martin Midstream Partners L.P. and subsidiaries as of December 31, 2015 and 2014, and the related consolidated statements of operations, changes in capital, and cash flows for each of the years in the three-year period ended December 31, 2015, and the effectiveness of internal control over financial reporting as of December 31, 2015, which reports appear in the December 31, 2015 annual report on Form 10-K of Martin Midstream Partners L.P.

/s/ KPMG LLP

Dallas, Texas

February 29, 2016