A grid-connected inverter (GCI) with LCL filters is widely used in photovoltaic grid-connected systems. While introducing active damping methods can improve the quality of grid-connected current (GCC), the influence of grid voltage disturbances can still significantly impact the quality of GCC, leading to stability degradation, especially in weak grid conditions. This paper proposes a grid-voltage-weighted feedforward control scheme based on the quasi-proportional resonance (QPR) controller. This scheme introduces compensatory terms with different proportional coefficients in the voltage feedforward, controlled by the QPR controller. Through a series of analyses, reasonable inverter parameters are first designed. Then, the proposed system model is built in Matlab Simulink. Through simulation experiments and comparisons with various types of operating conditions, the effectiveness of the proposed system scheme is validated. It minimizes the impact of grid voltage disturbances, suppresses the influence of grid harmonics on the control system, improves current quality, and enhances the stability of the GCI system.