In order to obtain the real-time information of the rotor of permanent magnet synchronous motor (PMSM) and improve the accuracy of speed and position estimation of the traditional speed sensorless control strategy of PMSM, a speed sensorless control scheme of PMSM in full speed range was proposed. A PMSM control system based on improved high-frequency injection algorithm and optimized sliding-mode observer is designed. In the low-speed region, the motor position error signal is extracted by the second-order generalized integrator. In the high-speed region, an improved reaching law sliding mode observer combined with a normalized phase-locked loop is used to eliminate the phase delay. In the full speed domain, the smooth weighting function based on the power function is used to dynamically adjust the weighting coefficient to realize the smooth switching of the algorithm. A system simulation model is built in MATLAB/Simulink to verify the effectiveness of the theoretical algorithm. The simulation results show that the hybrid control strategy of PMSM designed in this paper can realize the full-speed operation of PMSM under the conditions of no-load and load operation.