To improve the performance of the PMSM, a GSA based fractional oder QFT(FOQFT) control scheme for the PMSM is proposed. Firstly, the composite pseudo linear system, which is composed of the ANN-Inversion system and the controlled PMSM, is equivalent to a linear system with disturbance. Then, a FOQFT control scheme is designed based on the QFT method and fractional calculus, and the parameters of the fractional PID are designed by gravitational search algorithm (GSA). Finally, case study is fulfilled on a PMSM system and results show the effectiveness of the proposed control scheme.