This article introduces a simple model-predictive current control (MPCC) strategy for a three-level sparse five-phase voltage source inverter to suppress current harmonics and balance the neutral-point voltage. A total of 21 new virtual voltage vectors were developed as the control set of the MPCC, and an optimal voltage vector is selected among these 21 virtual voltage vectors to suppress output current harmonics. Since the switching states from the optimal voltage vector are determined according to the difference between the upper capacitor voltage and the lower capacitor voltage, the proposed MPCC guarantees the balanced neutral-point voltage without weighting factors and capacitor voltages prediction. Therefore, the proposed MPCC strategy can be implemented simply, and the computing time is significantly reduced. Simulation and experimental results are provided to verify the validity of the proposed strategy.