Permanent magnet synchronous motor (PMSM) is a multi-variables, non-linear and strong coupling system. A model reference adaptive controller (MRAC) for PMSM based on back propagation (BP) neural network (NN) is proposed to solve the shortcoming of traditional proportion integration (PI) control method, which is widely used in linear system. According to the proposed method, the simulation model is established and simulated with Simulink. The adaptive control of motor speed is achieved with the training of BP neural network. Simulation results show that the system has long response time, small overshoot and high static performance.