The differential algebraic sensorless control has the technical features of clear concept and low calculation amount. However, this method is particularly sensitive to motor parameters. Therefore, a differential algebraic sensorless control strategy combined with algebraic parameter identification is proposed and applied to surface mounted permanent magnet synchronous motor (SMPMSM) drive system in this paper. Without the signal injection, the proposed method can promptly and accurately realize the online simultaneous identification of stator resistance and inductance based on the different torque conditions of system, and then the motor parameters used in the differential algebraic sensorless control are updated in time. In addition, the tracking differentiator is designed to accurately obtain the first-order differential of the stator current signal with noises for rotor position estimation. Finally, the effectiveness of the proposed sensorless control method is validated by the simulation results.