Exhibit 23.1 Consent of Public Accountant

We consent to the incorporation by reference in the registration statements on Form S-3 (No. 333-193715 and No. 333-183481) and on Form S-8 (No. 333-140152) of Martin Midstream Partners L.P. of our reports dated March 3, 2014, with respect to the consolidated balance sheets of Martin Midstream Partners L.P. and subsidiaries as of December 31, 2013 and 2012, and the related consolidated statements of operations, comprehensive income, changes in capital, and cash flows for each of the years in the three-year period ended December 31, 2013, and the effectiveness of internal control over financial reporting as of December 31, 2013, which reports appear in the December 31, 2013 annual report on Form 10-K of Martin Midstream Partners L.P.