Modular multilevel matrix converter (M3C) is a new topology of AC-AC power converter,which has very broad application in low frequency transmission system,high-power asynchronous motor speed regulation and low offshore wind power transmission. Due to the power coupling effect of the two frequencies,the capacitive voltage of M3C bridge arms is prone to instability when the grid voltage is asymmetric. Firstly,the arm power of M3C under unbalanced input conditions is calculated,and the power distribution law among the arms of two different power balance method is summarized. On this basis,the influence of low-frequency circulating currents on the arm power is analyzed. Under the premise of ensuring the balance of input and output power of the system,a capacitor voltage balance control strategy based on the construction of circulating currents is proposed,which avoids the introduction of negative sequence current on the grid side. Under unbalanced conditions,the capacitor voltage can be quickly balanced by the capacitor voltage closed-loop control and direct power compensation strategy. The constructed low-frequency circulating currents only flow inside the converter,and will not affect the decoupling operation of M3C input and output sides. The effectiveness of the proposed control strategy is verified by a 220 kV,400 MW M3C system implemented in MATLAB.