Finite Control Set Model Predictive Control (FCS-MPC) method is an attractive to classical control method because of its fast-dynamic response and simple concept. In MPC the future values of the system variables and a cost function employing control objectives are calculated for all possible control actions. The switching action that minimizes the predefined cost function is selected to be applied for the next sampling period. This paper presents a model predictive control approach to regulate the output voltage of an ac-dc Matrix Converter (MC) in an indirect manner by imposing sinusoidal supply currents. The dc output voltage and the three-phase supply currents can be controlled simultaneously by solving a single-objective cost function. In this work, simple predictive supply current control method is described, and simulation results show that the proposed method performs quite well under steady-state and transient conditions.