Exhibit 24.1

                           LIMITED POWER OF ATTORNEY
                      FOR SECTION 16 REPORTING OBLIGATIONS

             Know all by these presents, that the undersigned hereby makes,
constitutes and appoints each of Manuel C. Alves Aivado, Donald V. Dougherty and
Rick Wanstall, signing singly and each acting individually, as the undersigned's
true and lawful attorney-in-fact with full power and authority as hereinafter
described to:

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

       (2)   do and perform any and all acts for and on behalf of the
undersigned which may be necessary or desirable to prepare, complete and execute
any such Form 3, 4, or 5, prepare, complete and execute any amendment or
amendments thereto, and timely deliver and file such form with the United States
Securities and Exchange Commission (the "SEC") and any stock exchange or similar
authority, including without limitation the filing of a Form ID, Update
Passphrase, or any other application materials to enable the undersigned to gain
or maintain access to the Electronic Data Gathering, Analysis and Retrieval
system of the SEC;

       (3)   seek or obtain, as the undersigned's representative and on the
undersigned's behalf, information regarding transactions in the Company's
securities from any third party, including brokers, employee benefit plan
administrators and trustees, and the undersigned hereby authorizes any such
person to release any such information to such attorney-in-fact and approves and
ratifies any such release of information; and

       (4)   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'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 relieving, nor is the Company assuming nor
relieving, any of the undersigned's responsibilities to comply with Section 16
of the Exchange Act.  The undersigned acknowledges that neither the Company nor
the foregoing attorneys-in-fact assume (i) any liability for the undersigned's
responsibility to comply with the requirement of the Exchange Act, (ii) any
liability of the undersigned for any failure to comply with such requirements,
or (iii) any obligation or liability of the undersigned for profit disgorgement
under Section 16(b) of the Exchange Act.

             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 June 24, 2019.


                              /s/ William T. McKee
                              -------------------------
                              Name: William T. McKee