Exhibit 4.2

Form of Lock-up Agreement

[___], 2018

Boustead Securities, LLC

6 Venture, Suite 265

Irvine, CA 92618

Re: Proposed Public Offering by Aptorum Group Limited

Ladies and Gentlemen:

The undersigned, a stockholder, director or officer of Aptorum Group Limited, a Cayman Islands company (the “Company”), understands that Boustead Securities, LLC (the “Representative”) will act as the representative of the underwriters, i.e., Boustead Securities, LLC, China Renaissance Securities (HK) Limited and AMTD Global Markets Limited (collectively, the “Underwriters”) to carry out an offering (the “Offering”) of the Company’s ordinary shares (the “Securities”). In recognition of the benefit that the Offering will confer upon the undersigned, and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the undersigned agrees with the Underwriters that, without the prior written consent of the Underwriters, during a period of six (6) months ¹ from the date on which the trading of the Securities on the NASDAQ Stock Exchange commences (the “Lock-Up Period”), the undersigned will not, without the prior written consent of the Representative, directly or indirectly (i) offer, pledge, sell, contract to sell, sell any option or contract to purchase, purchase any option or contract to sell, grant any option, right or warrant to purchase or otherwise transfer or dispose of any securities of the Company (including the issuance of shares of Securities upon the exercise of options) (collectively, the “Lock-Up Securities”), whether now owned or hereafter acquired by the undersigned or with respect to which the undersigned has or hereafter acquires the power of disposition, or file, or cause to be filed, any registration statement under the Securities Act of 1933, as amended, with respect to any of the foregoing or (ii) enter into any swap or any other agreement or any transaction that transfers, in whole or in part, directly or indirectly, the economic consequence of ownership of the Lock-Up Securities, whether any such swap or transaction described in clause (i) or (ii) above is to be settled by delivery of the Lock-Up Securities or such other securities, in cash or otherwise.

Notwithstanding the foregoing, and subject to the conditions below, the undersigned may transfer the Lock-Up Securities without the prior written consent of the Underwriters as follows, provided that (1) the Underwriters receives a signed lock-up agreement for the balance of the Lock-Up Period from each donee, trustee or transferee, as the case may be, (2) any such transfer shall not involve a disposition for value, (3) such transfers are not required to be reported in any public report or filing with the Securities and Exchange Commission, or otherwise and (4) the undersigned does not otherwise voluntarily effect any public filing or report regarding such transfers:

(1) as a bona fide gift or gifts; or

(2) to any trust or other entity for the direct or indirect benefit of, or wholly-owned by, the undersigned or the immediate family of the undersigned (for purposes of this lock-up agreement, “immediate family” shall mean any relationship by blood, marriage or adoption, not more remote than first cousin); or

(3) by will, other testamentary document or intestate succession to the legal representative, heir, beneficiary or a member of the immediate family of the undersigned; or

(4) by operation of law pursuant to a qualified domestic order or in connection with a divorce settlement.; or

(5) pursuant to a trading plan established or to be established pursuant to Rule 10b5-1 of the Exchange Act prior to the commencement of the initial public offering.

Notwithstanding the foregoing, if:

(1) during the last 17 days of the Lock-Up Period, the Company issues an earnings release or material news or a material event relating to the Company occurs; or

(2) prior to the expiration of the Lock-Up Period, the Company announces that it will release earnings results or becomes aware that material news or a material event will occur during the 16-day period beginning on the last day of the Lock-Up Period, the restrictions imposed by this lock-up agreement shall continue to apply until the expiration of the 18-day period beginning on the issuance of the earnings release or the occurrence of the material news or material event, as applicable, unless the Representative waives, in writing, such extension.

¹ Such period shall be reduced to 90 days for the Bond holders.

The undersigned hereby acknowledges and agrees that written notice of any extension of the Lock-Up Period pursuant to the previous paragraph will be delivered by the Representative to the Company and that any such notice properly delivered will be deemed to have been given to, and received by, the undersigned. The undersigned further agrees that, prior to engaging in any transaction or taking any other action that is subject to the terms of this lock-up agreement during the period from the date of this lock-up agreement to and including the 34th day following the expiration of the Lock-Up Period, it will give notice thereof to the Company and will not consummate such transaction or take any such action unless it has received written confirmation from the Company that the Lock-Up Period (as may have been extended pursuant to the previous paragraph) has expired.

The undersigned understands that, if the Offering shall terminate or be terminated prior to payment for and delivery of the Securities, the undersigned shall be released from all obligations set forth herein.

The undersigned also agrees and consents to the entry of stop transfer instructions with the Company’s transfer agent and registrar against the transfer of the Lock-Up Securities except in compliance with the foregoing restrictions.

The undersigned, whether or not participating in the Offering, understands that the Underwriters are proceeding with the Offering in reliance upon this lock-up agreement.

This lock-up agreement shall be governed by and construed in accordance with the laws of the State of New York, without regard to the conflict of laws principles thereof.

[Signature page follows]

Very truly yours,

(Name - Please Print)

(Signature)