This paper presents a model predictive control (MPC) scheme for quasi-Z-source (qZS) three-phase four-leg inverter. In order to cope with the drawbacks of traditional voltage source inverters (VSIs), a qZS three-phase four-leg inverter topology is proposed. This topology features a wide range of voltage gain which is suitable for applications in renewable energy-based power systems, where the output of the renewable energy sources varies widely with operating conditions such as wind speed, temperature, and solar irradiation. To improve the capability of the controller, an MPC scheme is used which implements a discrete-time model of the system. The controller handles each phase current independently, which adds flexibility to the system. Simulation and experimental studies verify the performances of the proposed control strategy under balanced and unbalanced load conditions as well as single-phase open-circuit fault condition.