Exhibit 31.2

Certification Pursuant to Section 302 of the Sarbanes-Oxley Act of 2002

I, Gregory K. Chow, certify that:

1. I have reviewed this Amendment No. 1 to Annual Report on Form 10-K/A of Aptose Biosciences Inc.; and

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.

Date: March 26, 2019

/s/ Gregory K. Chow

Name: Gregory K. Chow

Title: Senior Vice President and Chief Financial Officer