Abstract: In the weak power grid, the dynamic interaction between the phase-locked loop（PLL） and the current loop of the gridconnected converter will lead to small-signal（or harmonic） instability problems. To solve this problem, the small-signal modeling method is used to establish the equivalent impedance model of the grid-connected converter. On this basis, the converter impedance model is combined with the system stability judgment method, and the instability mechanism of the grid-connected inverter in the weak power grid is analyzed by using the pole variation trajectory and the Bode plot. For the multiple-input multipleoutput（MIMO） system, this paper proposes an active damping control strategy based on digital filters while considering multi-loop coupling. Three different types of filters are used to control the system stability and improve the system stability margin. The proposed control strategies can realize the decoupling between the phase-locked loop and the current loop, and effectively restrain the multi-loop coupling. At the same time, this paper also gives the specific implementation scheme of the control strategy and the parameter design method. And the impact of the control strategy on the multi-loop coupling part is analyzed. In addition, in order to study the effectiveness of the proposed control strategy under different conditions, this paper studies the system stability margin using the proposed control strategy under different grid strengths, phase-locked loop bandwidths, and current loop bandwidths.Then, the proposed control strategy is compared with the conventional methods. Finally, the correctness of the proposed theory is verified by the results of the simulation and the hardware-in-the-loop experiment.