In grid-connected LCL-filtered inverters, the dual-loop current control is widely used. The LCL resonance is highly damped by proper feedback of the capacitor current. To suppress low-frequency current harmonics, a grid-voltage feedforward is commonly used. However, the system performance with such control is declined when connecting to a weak grid. Phase and gain margins are largely reduced while the proportional feedforward is used. The margins get worse and instability is aroused if the derivative feedforward is further implemented. Besides, a negative impact on the rejection of grid-voltage-induced harmonics is produced. To improve the control performance in the weak grid case, an adaptive control has been proposed. Adopting the estimated grid impedance, the signal for the grid-voltage feedforward is modified and the controller is adjusted with an adaptive rule to maintain a good phase margin or a high bandwidth. Performances of the inverter with the typical and the proposed methods are compared. Simulation and experimental results have demonstrated that the grid-connected LCL-filtered inverter with the proposed method produced a high-quality current while large grid impedance existed.