Aiming at the problems of frequent overshoot and slow response time in space vector direct torque control system of permanent magnet synchronous motor, a control strategy based on a fast-super-twisting algorithm was proposed. Based on the traditional super-twisting algorithm, the fast terminal sliding mode reaching law (FTSMRL) is introduced in the strategy, which improves the algorithm’s robustness and convergence speed, suppresses the sliding mode chattering. The stability of the system is proved by using a quasi-quadratic Lyapunov function. Simulation results show that the proposed strategy can effectively improve the response speed and robustness of the system, and significantly reduce the system overshoot and sliding mode chattering.