In a weak grid, the line impedance variation will cause the resonant frequency of the LCL filter to shift towards lower frequencies, thus reducing the quality of the grid-connected current and affecting the power grid stability. To solve this problem, a hybrid active damping strategy with feedforward compensation is proposed for the neutral point clamped (NPC) LCL grid-connected inverter system. In order to reshape the output conductance of the grid-connected system, suppress the resonance spikes of the LCL filter and improve the adaptability of the grid-connected system to the weak grid. A first-order low-pass filter is designed in the grid-connected current loop, and an active damping control of grid-connected current based on a first-order high-pass filter is also proposed. Compared with the conventional capacitive current active damping, no additional sensors are required, and the use of a differential is avoided, which reduces the high-frequency noise. The use of passive resistors is reduced, which reduces the power loss of the grid-connected system. In addition, a point of common coupling (PCC) voltage feedforward strategy based on a low-pass filter is designed to suppress the background higher harmonics at PCC and improve the quality of grid-connected current. In this work, the robustness of the system is analyzed when the parameters of the LCL filter change. Finally, the virtual space vector modulation strategy is used to balance the neutral voltage of the DC bus. Simulation and experimental results show that the control strategy can effectively improve the adaptability of the system to the weak power grid, improve the quality of grid-connected current, and demonstrate strong stability. The THD can be decreased by 0.2% at least, and the improvements are more significant with larger line impedance; the THD is only 2.33% even at 10 mH line impedance.