According to the characteristics of permanent magnet synchronous motor (PMSM) system using quasiZsource inverter (qZSI), a finite control set model predictive control strategy was proposed in twophase stationary coordinate system. The reference value of inductance current was generated by controlling the capacitance voltage of quasiZsource network, and combining with the electromagnetic power feedforward value of PMSM. By predicting the inductance current value and introducing the subcost function, either the shootthrough (ST) case or nonST (NST) case was determined to realize the boost control of qZSI. In the NST case, the stator current of PMSM was predicted in eight switching states, and compared with the reference current generated by the speed closedloop control. The optimal switching state was selected to achieve the control of PMSM. The simulation results showed that the proposed control strategy could realize the boost control of qZSI and the speed control of PMSM. The system had good steadystate and dynamic performance.