Low frequency transmission system is a new type of AC transmission technology that combines traditional high voltage AC transmission and high voltage DC transmission, and adopts low frequency below power frequency. The core power converter of the system, the modular multilevel matrix converter (M3C), is a new AC/AC converter topology suitable for high voltage and high power. The fault-tolerant control of M3C is of great significance for improving the reliability of M3C system, but there are still problems with its fault-tolerant control strategy at present. The fault-tolerant control strategy with an optimal common mode voltage (CMV) injection method is proposed in this paper, which is able to maximize the input and output voltage ranges of the M3C after the failure of the non-redundant submodules. By calculating the relationship between the fundamental reference voltage and the maximum available voltage of each bridge arm branch in real time, the method can dynamically adjust the optimal CMV for injection to adapt to different fault situations. Finally, experiments are conducted in both MATLAB/Simulink and RT-LAB platforms to verify the correctness and effectiveness of the method proposed in this paper under single and multiple bridge arm branches fault conditions.