The modular multilevel matrix converter (M3C) is suitable for high-voltage and high-capacity AC/AC conversion due to its modular characteristics and easy expansion. However, the M3C topology has problems such as complex hardware circuits, mutual coupling of input and output frequencies, and special operating points, making it difficult to conduct modeling analysis and control strategy analysis. This paper utilizes dual-dq transformations to achieve decoupling between input and output frequencies, realizing independent control of both the input and output sides. Furthermore, addressing the issue of equal frequency operation in the M3C system, a frequency operation control strategy based on low-frequency circulating current injection was proposed. The proposed method does not require injecting common mode voltage or applying reactive power. Simulation results based on the M3C verify the effectiveness of the proposed method, and the dynamic and static performance of the control strategy is also validated.