To solve the problem of the sensorless control method of a permanent magnet synchronous motor, based on the study of a mathematical model for a permanent magnet synchronous motor and model adaptation theory, a reference model equation and adjustable model equation are derived according to the stator current equation. The correctness of the selected linear compensator matrix is strictly proved. Then, Popov’s super-stability theory is used to derive the speed adaptive law and prove its asymptotic stability. Based on the voltage closed-loop feedback MTPA weak magnetic control strategy, a simulation model of a MRAS control system based on stator current is built and combined with the principle of MRAS. Aiming to investigate the problem that the PI adaptive law in the traditional MRAS algorithm is not robust, super-twisting sliding mode control is introduced to replace the PI adaptive law. The observer based on STSM−MRAS is designed. The simulation model of the MRAS control system based on the super-twisting sliding mode is established. Under certain working conditions, the STSM−MRAS algorithm and the traditional MRAS algorithm are simulated and compared. The results show that the STSM−MRAS algorithm can improve the steady-state performance and robustness of a sensorless control system.