When a grid-connected inverter is connected to a weak grid, the system may be instable. An active damper, which synthesizes a damping resistor at the harmonic frequencies, can be connected to the point of common coupling (PCC) to damp the resonance and thus stabilize the system. In this paper, an adaptive tuning method of the virtual resistor is proposed, which can ensure the system stability while minimizing the port current of the active damper. Besides, to avoid the influence of the current loop on the characteristic of the virtual resistor, a compensation method for the harmonic current reference is proposed. The prototypes of a 5-kW grid-connected inverter and a 1-kVA active damper are built and tested to verify the effectiveness of the proposed control scheme of the active damper.