This paper presents a robust nonlinear generalized predictive control (RNGPC) strategy applied to a permanent magnet synchronous motor (PMSM) for speed trajectory tracking and disturbance rejection. The nonlinear predictive control law is derived by using a newly defined design cost function. The Taylor series expansion is used to carry out the prediction in a finite horizon. No information about the external perturbation and parameters uncertainties are needed to ensure the robustness of the proposed RNGPC. Moreover, to maintain the phase current within the limits using saturation blocks, a cascaded structure is adopted and an anti-windup compensator is proposed. The validity of the proposed control strategy is implemented on a dSPACE DS1104 board driving in real-time a 0.25 kW PMSM. Experimental results have demonstrated the stability, robustness and the effectiveness of the proposed control strategy regarding trajectory tracking and disturbance rejection.