At present, permanent magnet synchronous motor is widely used in industry. High performance permanent magnet synchronous motor control strategy has become the focus of research and development of researchers all over the world, and the position sensorless control of synchronous motor has become an important development trend in the future. Based on this, this paper proposes a sensorless vector control method of Luenberger observer in DQ coordinate system. Firstly, based on the vector control mathematical model of synchronous motor in DQ coordinate system, Luenberger observer in DQ coordinate system is constructed to calculate the motor speed and rotor position. Secondly, a simulation model is built to study the control performance of the sensorless system of permanent magnet synchronous motor. Finally, the feasibility and effectiveness of the Luenberger observer sensorless vector control method for PMSM are verified by the motor.