Modular multi-level converters (M2LCs) are typically controlled by using a hierarchical control scheme, where at least two loops are employed to control the load currents and circulating currents. This paper presents a new model predictive controller to control an M2LC with a single controller, which controls the load currents within tight bounds and minimizes capacitor voltage variations and circulating currents. The proposed controller uses the slope of load currents trajectories to emulate long prediction horizons. When switching is required due to violation of its bounds, a switch position that yields the trajectory with the minimum slope, relative to the reference trajectory, is determined and applied to the converter. Simulated performance of a three-phase three-level 2-MVA grid connected M2LC, during both steady-state and transient conditions, is presented to validate the feasibility of the proposed scheme.