Ultra Sparse Matrix Rectifier (USMR) is considered to be one of the simplest and compact three-phase PWM rectifiers. It is a buck three-phase AC-DC converter with one-quadrant operation capability. In this paper, Model Predictive Control (MPC) is applied to USMR supplying inductive load. The discrete time model of the system is derived. Then, the MPC algorithm for the proposed system is discussed. Finally, the system is simulated using Matlab. The performance of the proposed USMR controlled using MPC is compared to the one using Space Vector Modulation (SVM). Simulation results show that the MPC has more harmonic performance benefits than the SVM one. However, the efficiency of the system that uses MPC is slightly lower than the one that uses SVM, due to the built in switching loss minimization of the SVM.