In order to develop a sensorless PMSM driving and control system to replace the traditional position sensor,one sensorless PMSM vector control system mathematical model based on sliding mode observer(SMO)has been established by analyzing the theory of sliding mode control(SMC)and the mathematical model of permanent magnet synchronous motor(PMSM),and has built the sensorless PMSM vector control system simulation model which adopted id=0 vector control strategy and analyzed the simulation results.The results show that the slide mode observer method can estimate rotor position accurately,it can trace the current and torque rapidly,the correctness and feasibility of SMO theory are verified which applied on PMSM drive and control system.