In this study, a robust predictive power control (R-PPC) method for an N*3-phase permanent magnet synchronous motor (PMSM) is developed in the field of flywheel energy storage systems application, which can effectively improve robustness against inductance parameter mismatch and compensate for the one-beat delay. Firstly, the mathematical model of the N*3-phase PMSM is illustrated, and the topological structure of the N*3-phase PMSM is established. The R-PPC method of the N*3-phase PMSM is then proposed by using the d−q axis current robust predictive control theory. Robustness factors are adopted to modify the current response values in the proposed robust predictive power controller, which can obtain excellent current control performance under the inductance parameter mismatch. Moreover, the next current predicted value is used to replace the current sampled value in the proposed R-PPC method to eliminate the one-beat delay. Finally, comparative simulation and experimental results verify that the proposed R-PPC method can achieve excellent current track performance and smaller torque ripple under both the charge state and discharge state.