Under weak grid conditions, the variation of the grid impedance will affect the steady-state and dynamic performance of the LCL-filtered grid-connected inverter and even make the inverter unstable. To ensure the system stability and further improve the dynamic performance in a weak grid, a control parameter design method with multi-constrains considering the system bandwidth for the current controller and active damping is proposed in this paper. First, based on the current controller and active damping with only grid current feedback, the effects of control parameters and grid impedance on the LCL resonant suppression and the performance of the inverter are analyzed. Moreover, the parameter constraints of the controllers are derived considering the grid impedance, including stability, resonance suppression, and margin constraints. Furthermore, as the system bandwidth affects the dynamic performance of the inverter, combined with the obtained multi-constraints, the optimal control parameters are determined by achieving the maximum bandwidth of the system against the impedance variation. Compared with other two methods, when the proposed method is applied, the system can operate with a better dynamic and steady-state performance. Finally, experiments are performed on a 2 kW three-phase grid-connected inverter in the weak grid, which verify the effectiveness of the parameter design method proposed in this paper.