The modular multilevel matrix converter (M3C) applied to a low frequency alternating current (LFAC) transmission system is investigated. Due to the complexity and tight coupling of the converter, a novel hierarchical model predictive control (MPC) scheme with a cascaded structure of power control, capacitor voltage averaging and balancing control for M3C is proposed. The terminal behavioral model of M3C is derived out and the fast separated space-vectors approximation method is realized. The proposed scheme clearly achieves the system-level multi-objective control without the empirical procedure of the weighting factor design and significantly reduces the computational cost. This is the first time to apply the MPC to a converter in a hierarchical structure. Simulation results of a 7-level M3C are provided to illustrate the system's performance.