The Z-source inverter has been widely used because it overcomes the shortcomings of the conventional voltage-type inverter that can only be stepped down and cannot be boosted, and must be added to the dead time. This paper proposes a single-cycle and LCL active damping control scheme to control the grid connection of three-phase Z-source inverter. Compared with the traditional PWM control, the singlecycle control has the advantages of simple structure, low-harmonic content and high output power quality while the LCL filter performs better than the LC and L filters, but the resonance peak reduces system stability. Therefore, the active damping method is adopted and the filter capacitor current loop and the grid-connected current loop are introduced to form a double loop control structure to suppress the adverse effect of the resonance peak on the system stability. Finally, simulations under Simulink verify the feasibility and effectiveness of the proposed scheme.