Abstract: In practical terms, a large number of distributed power sources are connected to the grid, so that the variations in weak grid impedance can no longer be ignored. To enhance the robustness of grid connected converter against the variations in grid impedance, an improved active damping control strategy is proposed to increase the positive and negative damping boundary frequencies. A analysis was conducted on the influence mechanism of the digital control delay on the system stability. In order to eliminate the negative influence of the delay on the active damping effect, a phase compensator was introduced into the damping control link to optimize the strategy, thus increasing the boundary frequencies of positive and negative damping to get closer to Nyquist frequency. The feedback coefficient for a wide variation range in grid impedance was designed to address the issue of resonant frequency shift caused by minor changes in grid impedance. The strong robustness of grid connected converter to grid impedance in weak grids was realized simultaneously. The analysis on the performance of the system reveals that when the LCL resonant frequency varies within Nyquist frequency, the system can maintain stability with this method. The research results demonstrate that the proposed active damping control strategy can significantly improve the adaptability to the impedance changes in the weak grid. The effectiveness of the proposed strategy and parameter design in achieving high robustness of weak grids is finally verified through simulation and experimental results.