The superior high-frequency harmonic suppression capability of LCL filters renders them a widely utilized component in grid-connected processes. Nevertheless, the perturbation of pertinent state variables has the potential to impact the stability of LCL grid-connected systems in the presence of weak grids. In order to address the aforementioned influencing factors, a composite active damping control strategy is put forth for consideration. The strategy combines current feedback from the capacitor and voltage feedforward from the common coupling point, effectively suppressing the resonance spikes of the LCL filter while reducing the resonance point shift for the digital delay in controlling. The harmonic distortion rate of the grid-connected current and voltage are reduced, thereby improving the power quality and robustness of this system. Simulation is then used to verify the proposed control strategy, which demonstrates that it is an effective solution with good interference immunity, dynamic performance, and steady-state performance under different grid impedance and grid impedance mutation conditions.