This paper proposes a robust nonlinear predictive current control (RNPCC) method for permanent magnet synchronous motor (PMSM) drives, which can optimize the current control loop performance of the PMSM system with model parameter perturbation. First, the disturbance caused by parameter perturbation was considered in the modeling of PMSM. Based on this model, the influence of parameter perturbation on the conventional predictive current control (PCC) was analyzed. The composite integral terminal sliding mode observer (SMO) was then designed to estimate the disturbance caused by the parameter perturbation in real time. Finally, a RNPCC method is developed without relying on the mathematical model of PMSM, which can effectively eliminate the influence of parameter perturbation by injecting the estimated disturbance value. Simulations and experiments verified that the proposed RNPCC method was able to remove the current error caused by the parameter perturbation during steady state operation.