The Modular multilevel matrix converter (M3C) is a direct ac-ac power converter that presents several features such as scalable and flexible structure, high efficiency, fault-tolerant capability, and high power quality. However, this converter requires a complex control strategy to govern the cluster currents and balance the internal floating capacitor voltages among clusters and cells. To fulfill these requirements, this work proposes a long-horizon sequential finite-control-set model predictive control (sFCS-MPC). The resulting predictive strategy is formulated to perform both the local cell balancing control and to regulate cluster currents of the M3C in a unified control algorithm, considering the nonlinear and coupled dynamic model of each cluster. Additionally, the total available combinations and the average cell switching frequency are reduced. The proposed sFCS-MPC is implanted for a prediction horizon from one to four, and compared with some previous FCS-MPC approaches. Experimental results on a 3 kW prototype are provided to demonstrate the effectiveness and high-quality performance of the proposed strategy.