This paper proposes a direct model predictive control (MPC) strategy to control the bidirectional quasi-Z-source inverter (BqZSI) driving a permanent magnet synchronous machine (PMSM) for electric vehicle applications. The dq machine currents are simultaneously controlled with the capacitor voltage and inductor current of the dc side. The physical model of the BqZSI with PMSM is first derived which encompasses different operating modes and states of the BqZSI. To examine the performance of the proposed control scheme at steady-state and transient operation, simulations based on MATLAB/Simulink are conducted. The results indicate that the proposed control scheme offers a very good steady-state performance as well as fast dynamic responses during transients.