The modular multilevel matrix converter (M3C) is the core equipment for fractional frequency transmission system (FFTS). The AC-AC conversion of M3C leads to direct coupling of the ac electrical quantities at different frequencies,causing complex harmonic distribution. In order to analyze the harmonic characteristics of the M3C,the analytical expression of the sub-module capacitor ripple voltage is derived based on the operating principle of M3C at first. On this basis,the analytical formulas of the nine bridge arms currents harmonics are derived,taking into account the coupling of all four frequency components of the capacitor voltage. The relationships between the multi-frequency harmonic currents of bridge arm and the system currents on two sides are analyzed,as well as the key factors affecting the amplitudes of ripple voltage/harmonic current are discussed. The results show that in steady-state,the currents at frequencies ω₁ and ω₂ flow into the ac systems as the positive-sequence fundamental currents; the currents at frequencies 3ω₁ and 3ω₂ flow into the ac system as the zero-sequence components;the remaining harmonics are circulated in the converter. A zero-sequence current mitigation control strategy for the M3C is proposed. The accuracy of the theoretical harmonic analysis and the effectiveness of the control strategy are verified by simulations in Matlab/Simulink.