Abstract: The flexible low-frequency transmission system（LFTS） based on the modular multilevel matrix converter（M3C） has the capability of two-phase operation on the low-frequency side, but its control strategy needs special design. First, this paper describes the basic condition of two-terminal flexible LFTS and the basic requirements of two-phase operation, and proposes a mathematical model of M3C for fundamental-frequency and low-frequency side input decoupling control and bridge arm circulating current control. In order to balance the capacitor voltage of bridge arm sub-modules under the asymmetric operation condition on the low-frequency side, a dual low-frequency circulating current control method for rebalancing the bridge arm power of M3C is proposed. The input current control strategy on the low-frequency side of V/f and PQ stations under the two-phase operation condition is given, respectively. Then the control of M3Cs for two stations is realized by completely independent current control of nine bridge arms in the static coordinate system. Finally, the simulation model of a two-terminal flexible LFTS is built in the realtime digital simulation（RTDS） system, and simulation tests are carried out for typical operation conditions such as the steady-state operation, the dynamic operation and the AC system asymmetric fault. The simulation test results show that the proposed control strategy can effectively meet the requirements of two-phase operation on the low-frequency side of the two-terminal flexible LFTS.