The phase-locked loop (PLL) has an important effect on the system stability of grid-connected converters in weak grids. In the literature, parameter tuning methods and stabilizing control strategies have been proposed to deal with this problem. However, most of them target at tuning parameters of PLL or mitigating the negative damping as well as the phase lag introduced by the PLL, while the interactions between the PLL and the current control and the cross coupling effects are still not fully explored in the design procedure of stabilizing control. To address this issue, this article extends the study of the interaction between the PLL and the current control using a multiple-input multiple-output (MIMO) model, and then proposes a design criterion of the stabilizing control using design-oriented analysis from the perspective of MIMO impedance model. A category of stabilizing control schemes that uses different types of biquad filters is proposed following the criterion, which not only improves system stability but also removes the coupling between the PLL and the current control according to the sensitivity analysis. Hardware-in-the-loop and experimental results are provided to verify the effectiveness of the proposed control schemes.