In this paper, a Model Predictive Control (MPC) strategy is applied to a Multilevel Current Source Inverter (MCSI) and its associated current source. The controller uses a discrete-time model of the entire system in order to predict the future behavior for each of the available switch states. The system is composed of a multilevel inverter, a buck converter, an output filter and a load. Each of the calculated values is used to minimize a set of predefined control objectives within a multiterm cost function. It includes costs associated with the switching frequency and reference tracking. This allows to control not only the output voltages of the load, but also the current source and the balance of the internal currents of the inverter. Simulation results show a good performance and fast dynamics with a low switching frequency of all the switches involved. These features make the proposed controller a suitable option for use with high power converters.