The use of mechanical sensors would increase the cost and failure rate of the speed control system. The permanent magnet synchronous motor (PMSM) position sensorless vector control system was designed based on model reference adaptive system (MRAS). The MRAS algorithm was used to obtain the speed and position of the PMSM vector speed control system. Appropriate adaptive law was selected for the system. The system was proved to satisfy the Popov hyperstability condition, ensuring the asymptotic stability of the system. Finally, simulation model was built by using MATLAB/Simulink. The simulation results showed that the designed position sensorless speed control system had good control performance under the conditions of sudden load change and dynamic speed change.