In the application of permanent magnet synchronous motor (PMSM), the failure of current sensor usually leads to the unstable operation of a motor system and affect the normal operation of the system. A current sensorless PMSM control method is proposed in this paper, based on improved adaptive backstepping observer. Firstly, the recursive least squares identification inductance is combined with the adaptive backstepping observer to estimate the d-q axis current and stator resistance. Then, its stability is proved by Lyapunov method and its convergence is analyzed. Finally, Comparisons are carried out between the current sensor control and the observer without inductance identification. Simulation results show that the current and speed tracking response of the current sensorless drive system achieves expected effect, and has good dynamic performance and strong robustness.