The phase margin of the output impedance is very low when the traditional grid voltage feed-forward control is used in an inverter under a non-ideal grid, and it cannot suppress the interference of the grid-voltage’s harmonic to the output current of the inverter well. Therefore it is difficult to guarantee the quality of grid-connected current. This paper presents a control strategy to improve the grid-connected current quality of inverters under non-ideal grid conditions. First, the output impedance model of LCL inverters with traditional grid voltage feed-forward under a PR controller is established, and an improved grid voltage feed-forward strategy based on a band-pass filter is proposed to improve the robustness of inverters to grid impedance. At the same time, a multi-harmonic compensator is connected in parallel with the PR controller. It can not only improve the robustness of the inverters to the impedance of the power grid, but also effectively restrain the interference of the harmonic voltage to the grid-connected current. Therefore, the quality of grid-connected current under the non-ideal grid can be improved. Finally, the effectiveness of the proposed method is verified by simulation and experiment. This work is supported by Youth Science Fund of National Natural Science Foundation of China (No. 51607179).