When a grid-connected inverter (unit) is connected to a weak grid, the wide range of grid impedance variation may lead to system instability. To solve this problem, a centralized active damping device is configured in parallel at the point of common coupling (PCC) to simulate the external characteristics of damping resistance, thus realizing the suppression of resonance between the grid-connected inverter and grid. In this paper, an adaptive adjustment method for virtual impedance value based on active damping device is proposed, which not only ensures the system stability, but also minimizes the current flowing in the active damping device. At the same time, a current harmonic reference compensation method is proposed, which can reduce the influence of current closed-loop on the virtual impedance characteristics and further improve the damping effect. A 5 kW grid-connected inverter and a 1 kW active damping device were built in a laboratory to verify the effectiveness of the proposed control scheme.