With increasing demands for higher efficiency, wider speed regulation range, and enhanced robustness in motor control systems driven by advancements in high-end manufacturing, new energy technologies, and artificial intelligence, conventional voltage-source inverters (VSI) face limitations. Specifically, their modulation index varies with fluctuations in battery voltage, leading to significant harmonic distortion—particularly under light-load conditions with low modulation indices. The Z-source inverter (ZSI), featuring a unique shoot-through state control mechanism and inherent boost-buck capability, offers improved flexibility and reliability for permanent magnet synchronous motor (PMSM) drive systems. In this paper, a closed-loop control system for a ZSI-fed PMSM is proposed based on modulated model predictive control (MMPC). A model predictive control strategy is employed to dynamically regulate the shoot-through duty ratio, while a modulation index feedback-based closed-loop correction mechanism is introduced to adaptively adjust the DC-link voltage. This approach ensures optimal system efficiency under maximum modulation index conditions, effectively enhancing dynamic performance, disturbance rejection, and overall system robustness. Simulation results validate the feasibility and superiority of the proposed variable DC-link voltage control scheme and the MMPC strategy in extending the motor speed regulation range and suppressing harmonic distortion.