Model predictive control (MPC) is an advanced kind of control strategy. The core of the algorithm is predictable future dynamic model, online iterative optimization calculation and rolling implementation control effect and feedback correction of model error. A predictive current control method based on continuous control set model predictive control (CCS-MPC) is investigated in this paper for the permanent magnet synchronous motor (PMSM). A Luenberger state observer is proposed to realize the current control without static error, caused by parameter mismatch and sampling delay. Simulation results verify the effectiveness of the proposed current control approach.