POWER OF ATTORNEY

KNOWN ALL MEN BY THESE PRESENTS, that the undersigned hereby constitutes and
appoints each of Laura Barton and Mark Gordon, signing singly, the undersigned
true and lawful attorney-in-fact, to:


     (1)   execute for and on behalf of the undersigned, in the undersigned
           capacity as an officer and/or director of Odyssey Marine Exploration,
           Inc. (the Company), Forms 3, 4 and 5 in accordance with Section 16(a)
           of the Securities Exchange Act of 1934 and the rules thereunder;

     (2)   do and perform any and all acts for and on behalf of the undersigned
           which may be necessary or desirable to complete and execute any such
           Forms 3, 4 and 5 and timely file such form with the United States
           Securities and Exchange Commission and any stock exchange or similar
           authority; and

     (3)   take any other action of any type whatsoever in connection with the
           foregoing which, in the opinion of such attorney-in-fact, may be of
           benefit to, in the best interest of, or legally required by, the
           undersigned, it being understood that the documents executed by such
           attorney-in-fact on behalf of the undersigned pursuant to this power
           of attorney shall be in such form and shall contain such terms and
           conditions as such attorney-in-fact may approve in such attorney-in-
           fact discretion.

     The undersigned hereby grants to each such attorney-in-fact full power and
authority to do and perform any and every act and thing whatsoever requisite,
necessary or proper to be done in the exercise of any of the rights and powers
herein granted, as fully to all intents and purposes as the undersigned might or
could do if personally present, with full power of substitution or revocation,
hereby ratifying and confirming all that such attorney-in-fact, or such
attorney-in-fact substitute or substitutes, shall lawfully do or cause to be
done by virtue of this power of attorney and the rights and powers herein
granted. The undersigned acknowledges that the foregoing attorney-in-fact in
serving in such capacity at the request of the undersigned, are not assuming,
nor is the Company assuming, any of the undersigned responsibilities to comply
with Section 16 of the Securities Exchange Act of 1934.

     This power of attorney shall remain in full force and effect until the
undersigned is no longer required to file Forms 3, 4 and 5 with respect to the
undersigned holdings of and transactions in securities issued by the Company, un
less earlier revoked by the undersigned in a signed writing delivered to the
foregoing attorneys-in-fact.

     IN WITNESS WHEREOF, the undersigned has caused this power of attorney to be
executed as of this 29 day of August 2016.

                                        Name: Jay Nudi

                                        /s/ Jay Nudi
                                        ---------------------
                                        Signature

STATE OF FLORIDA

COUNTY OF HILLSBOROUGH

The foregoing instrument was acknowledged before me this 29 day of August,
2016 by Jay A. Nudi who is personally known to me.

[SEAL]                                  /s/ Robert A. Deknes, Jr
                                        ----------------------------
                                        Robert A. Deknes, Jr
                                        Notary Public
                                        My Commission  #FF 114395
                                        Expires July 7, 2018