Poor robustness of the traditional PI control, and chattering and less poor robustness of the traditional non-singular fast terminal control occur in permanent magnet synchronous motor (PMSM). To solve these problems, a non-singular fast terminal sliding mode (NFTSM) control strategy is adopted in the speed loop. In addition, a high gain extended observer is introduced to observe the matching disturbance of the system in real time. Then the observed value is used as feedforward compensation of the current, and the anti-disturbance capability of the system is improved. At the same time, a deadbeat current predictive control strategy is adopted in the current loop. Dynamic response is better and harmonic components are smaller in the current loop. Simulation results show that the proposed control method can effectively improve the robustness of the system and solve the problem of excessive sliding mode chattering.