In order to improve the performance of permanent magnet synchronous motor (PMSM), the magnetic steel thickness, eccentric distance and pole arc coefficient are selected as variables to optimize the cogging torque and air-gap magnetic density distortion rate of the motor. Firstly, the sample space of each variable is obtained through orthogonal design method simulation. Secondly the support vector machine (SVM) is used to fit the simulation data set to obtain the fitting model of cogging torque and no-load air gap magnetic density distortion rate. Finally, multi-objective cultural differential evolution (MOCDE) algorithm is used to optimize the model. A 48-slot 8-pole PMSM is taken as an example for simulation verification. The simulation results show that the model based on SVM is accurate and reliable, and combined with MOCDE algorithm, it can effectively optimize the cogging torque and air-gap magnetic density distortion rate.