The LCL grid-connected inverter has the ability to attenuate the high-frequency current harmonics. However, the inherent resonance of the LCL filter affects the system stability significantly. To damp the resonance effect, the dual-loop current control can be used to stabilize the system. The grid current plus capacitor current feedback system is widely used for its better transient response and high robustness against the grid impedance variations. The weighted average current (WAC) feedback scheme is capable to provide a wider bandwidth at higher frequencies but show poor stability characteristics under weak grid scenarios. To overcome this shortcoming, the improved WAC damping method is proposed with an additional capacitor current feedback loop. In this paper, a systematic parameter design guideline for the optimal selection of the current loop proportional resonant controller and the additional capacitor current feedback coefficient are presented for the improved WAC feedback control strategy. The satisfactory range of the system control parameters can be obtained under different delay conditions to meet the system performance specifications. The improved WAC method enhances system robustness under weak grid scenarios, and the stability and robustness have been enhanced under control delay. Finally, the experimental results are presented to validate the effectiveness of the proposed improved WAC control strategy and the parameter design method.