Abstract: The reasons for low-order harmonics in the input current of a 3-1 matrix converter (3-1MC) were analyzed, and the relationship of modulation function between the output side and power compensation side was derived. The single grid-side current feedback control strategy cannot be used to control the input current component without steady state error under unbalanced input. It was proposed that input current positive sequence and negative sequence dq axis decoupling for the inner loop, and output side and compensation voltage weighted synthesis for the outer loop in the double closed-loop decoupling control strategy. The experimental and simulation results show that the proposed scheme not only facilitates power compensation using a 3-1MC but also effectively suppresses low-order harmonics in the input current and the output voltage under unbalanced input. Moreover, the proposed strategy improves the practicality of 3-1MCs.