Since motor parameter disturbance could cause current static error and oscillation in PWM predictive current control of permanent magnet synchronous motor (PMSM), PWM predictive current control based on Luenberger observer was proposed. Firstly, system parameter disturbance was introduced into the motor voltage equation, and Luenberger observer with excellent performance in parameter perturbation was constructed to observe the system disturbance. Then, Luenberger disturbance observer was discretized, and system stability was analyzed by pole assignment. Finally, disturbance from the observer was introduced into the voltage equation with parameter disturbance to provide realtime disturbance compensation for the algorithm. Simulation results showed that the proposed algorithm could rapidly observe the disturbance of the system without static error, effectively avoid the current static error and oscillation caused by inductance parameter error, and improved the robustness of current prediction algorithm.