Abstract: The problem of complete synchronization for a novel class of fractional-order (FO) delayed financial chaotic systems was discussed. Three feedback gain controllers with time delay were designed in the response system. Based on FO Razumikhin theorem and fractional inequality, a sufficient condition for the complete synchronization of the drive-response system was obtained. The results showed that the state of the response system would be complete synchronized with the state of the drive system, and the state of the error system would be stable, which shows that the design of the controller is effective. Ultimately, numerical verifications were given to verify the correctness of the results obtained.