There is uncertainty of the nonlinear term in a permanent magnet synchronous motor, as well as of the influence of parameter perturbation and load disturbance on mechanical angular frequency, rotational speed and system control during operation. To meet the requirements of high precision and high stability speed regulation application, an adaptive backstepping robust control strategy of PMSM based on grey wolf optimization is proposed. The nonlinear backstepping control is applied to solve the nonlinear problem of the motor, and grey wolf optimization is applied to the adaptive backstepping algorithm to realize the adaptive adjustment and tracking of the motor speed to the expected value, thus obtaining better dynamic response and robustness. A mathematical model of a permanent magnet synchronous motor including parameter perturbation and output side load perturbation is established. Then a backstepping controller satisfying Lyapunov stability is designed. Then the parameters of the backstepping controller are optimized by grey wolf algorithm to further improve the stability and robustness of the system. The simulation results verify the controller's good speed tracking and anti-interference adjustment effects and the effectiveness of the method. This work is supported by the Shanghai Science and Technology Innovation Action Plan (No. 19DZ2204700) and the Innovation and Entrepreneurship Incubation Fund Project of Zhejiang Electric Power Company.