This paper presents a model predictive control (MPG) scheme for quasi-Z source (qZS) three-phase four-leg inverters. In order to cope with drawbacks of the traditional voltage source inverters (VSI)s, the qZS three-phase four-leg inverter topology is proposed in this study. To improve control capability of the controller, the MPG scheme is used. The proposed MPG is based mainly on the discrete-time model of the whole system. The proposed controller handles each phase current independently. As a result of this, the proposed qZS four-leg inverter has fault tolerant capability, for example if one leg fails the others can work normally. Simulation studies were performed to verify the steady-state and transient-state performances of the proposed control strategy under balanced/unbalanced reference currents and load conditions.