Exhibit 12.1



Certification

Pursuant
to Rule 13a-14(a) of the Exchange Act



I,
Ian Huen, certify that:



| | 1. | I
    have reviewed this annual report on Form 20-F, as amended by Amendment No. 1 thereto, of Aptorum Group Limited;
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| | 2. | Based
    on my knowledge, this report does not contain any untrue statement of a material fact or omit to state a material fact necessary
    to make the statements made, in light of the circumstances under which such statements were made, not misleading with respect
    to the period covered by this report;
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| | 3. | Based
    on my knowledge, the financial statements, and other financial information included in this report, fairly present in all
    material respects the financial condition, results of operations and cash flows of the company as of, and for, the periods
    presented in this report;
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| | 4. | The
    company’s other certifying officer(s) and I are responsible for establishing and maintaining disclosure controls and procedures
    (as defined in Exchange Act Rules 13a-15(e) and 15d-15(e)) and internal control over financial reporting (as defined in Exchange
    Act Rules 13a-15(f) and 15d-15(f)) for the company and have:
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| | a. | Designed
    such disclosure controls and procedures, or caused such disclosure controls and procedures to be designed under our supervision,
    to ensure that material information relating to the company, including its consolidated subsidiaries, is made known to us
    by others within those entities, particularly during the period in which this report is being prepared;
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| | b. | Designed
    such internal control over financial reporting, or caused such internal control over financial reporting to be designed under
    our supervision, to provide reasonable assurance regarding the reliability of financial reporting and the preparation of financial
    statements for external purposes in accordance with generally accepted accounting principles;
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| | c. | Evaluated
    the effectiveness of the company’s disclosure controls and procedures and presented in this report our conclusions about the
    effectiveness of the disclosure controls and procedures, as of the end of the period covered by this report based on such
    evaluation; and
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| | d. | Disclosed
    in this report any change in the company’s internal control over financial reporting that occurred during the period covered
    by the annual report that has materially affected, or is reasonably likely to materially affect, the company’s internal control
    over financial reporting; and
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| | 5. | The
    company’s other certifying officer(s) and I have disclosed, based on our most recent evaluation of internal control over financial
    reporting, to the company’s auditors and the audit committee of the company’s board of directors (or persons performing the
    equivalent functions):
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| | a. | All
    significant deficiencies and material weaknesses in the design or operation of internal control over financial reporting which
    are reasonably likely to adversely affect the company’s ability to record, process, summarize and report financial information;
    and
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| | b. | Any
    fraud, whether or not material, that involves management or other employees who have a significant role in the company’s internal
    control over financial reporting.
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|Date: April 22, 2019 | By: | /s/
    Ian Huen
|-------------------- | --- | ----------------
|                     |     | Name:           
|                     |     | Title: