The grid-connected inverter with a LCL filter has the ability of attenuating the high-frequency current harmonics. The current distortion caused by harmonics in the grid voltage is difficult to be eliminated. Applying proportion feedforward of the grid voltage can suppress the effect of grid voltage harmonics. However, weak grid is commonly seemed as a voltage source which contains a grid impedance and background harmonics, the closed-loop control and the proportion feedforward control are coupling with each other because of the existence of grid impedance. Proportion feedforward control will introduce a positive feedback loop, which will worsen the quality of the system. In this paper, a novel grid voltage feedforward control strategy was proposed. This novel control strategy is to add a low-pass filter to the grid voltage feedforward channel, which could improve the adaptability to the grid impedance. The correctness of the theoretical analysis and effectiveness of the proposed control strategy are verified by the simulation and experimental results.