POWER OF ATTORNEY

      KNOW ALL MEN BY THESE PRESENTS, that the undersigned constitutes and
appoints Harold H. Shlevin, PhD, Jack W. Callicutt, Robert E. Tritt and Derek B.
Swanson, and each of them, his true and lawful attorneys-in-fact and agents,
with full power of substitution, for him and in his name, place and stead, in
any and all capacities, to:

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

2.   do and perform any and all acts for and on behalf of the undersigned that
may be necessary or desirable to complete and execute any such Form 3, 4 or 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 any 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's 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's 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 attorneys-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's 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's holdings of and transactions in securities issued by the Company,
unless 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 3rd day of March, 2020.


                                          /s/ Pol F. Boudes
                                          -----------------
                                          Name: Pol F. Boudes, M.D.