Most matrix converters use indirect control, which includes a three-phase virtual AC/DC converter and a virtual inverter, to control their nine AC switches. However, matrix converters do not use electrolytic capacitors to store energy. As a result, unbalanced three-input voltages directly cause unbalanced three-phase output voltages, which deteriorate the performance of IPMSM drive systems. To solve this problem, this paper proposes an improved method, which includes inverter stage control and AC/DC stage control, for matrix converter-based IPMSM drive systems under unbalanced three-phase input voltages. The inverter stage control adjusts the duty cycles of the virtual inverter to compensate for the fluctuations of the virtual DC-bus voltage. Therefore, the harmonic currents of the IPMSM are significantly reduced, and the speed ripples of the IPMSM are reduced as well. The AC/DC stage control uses a virtual AC/DC converter to control the threephase input currents near sinusoidal waveforms with a unity power factor. Finally, a hybrid algorithm that combines the inverter stage control and the AC/DC stage control is demonstrated. A digital signal processor, type SH 7237, and a field programmable gate array, type 10M16SAU16917G, are used in parallel as the computational and control center.