This paper aims to use a three-phase quasi-Z-source indirect matrix converter (QZSIMC) to expand the voltage gain for application in a Permanent Magnet Synchronous Motor (PMSM) drives. In this converter, a unique quasi-Z-source network (QZSN) connects the three-phase input voltage to conventional indirect matrix converter (IMC) in order to boost the supply voltage for PMSM because of limited voltage gain of IMC. Dual space vector modulation (SVM) is utilized to control the QZSIMC. The amplitude of output voltage for quasi-Z-source network is raised by the shoot-through of the rectifier stage, so the system voltage gain becomes greater. Through selecting the optimized value of shoot through duty ratio (<em>D</em>) and modulation index of the rectifier stage (), the drive system can automatically regulate the output voltage of QZSIMC during conditions of voltage sag , step change in load torque and reference speed change when the required voltage gain of QZSIMC is more than 0.866 depending on input voltage and required output voltage.The vector control technique based on closed loop speed control is proposed to control speed of the motor from zero to rated speed which is combined with the proposed converter to obtain the motor drive. The simulation results with MATLAB /Simulink 2015 are obtained to validate performance of PMSM drive.