The Modular Multilevel Converter (MMC) is a newly introduced multilevel converter topology with high modularity and scalability, suitable for a wide range of voltage/power applications. This paper proposes a model predictive control (MPC) strategy to eliminate the circulating currents and carry out the voltage balancing task of an MMC. A discrete-time mathematical model of an MMC is derived and a predictive model is developed. The salient feature of the proposed control strategy is that it enables precise ac-side current control, capacitor voltage balancing, and circulating current mitigation of an MMC, simultaneously, with a simple implementation procedure. Performance of the proposed MPC-based strategy for a five-level grid-connected MMC unit is evaluated based on time-domain simulation studies in the PSCAD/EMTDC software environment. The reported study results demonstrate satisfactory response of the system operating based on the proposed MPC strategy, under various conditions.