Abstract: Modular multilevel matrix converter (M3C) is a kind of AC/AC converter topology applied in high voltage and high power fields. Many parameters need to be adjusted in the current multi-loop control scheme and there is no strict stability proof for them, which can not guarantee the global stability of the closed-loop system. In this paper, the state space model of M3C system is established, and the state-error feedback controller is designed according to the Lyapunov theory. This method can ensure the global asymptotic stability of the system, and the parameters can be adjusted in a simple method and the control performs well. The simulation and experimental results verifies the feasibility and effectiveness of the designed M3C control strategy.