Abstract: The equivalent impedance of the inverter’s Norton equivalent circuit is coupled with the power system, which is the source of the resonance that caused by the grid-connected inverter. Therefore, this paper studied the impedance characteristic of inverters and proposed a stability criterion based on the impedance characteristic curve. Firstly, combined the theoretical analysis and the physical measurement results of the inverter’s equivalent impedance, the impedance characteristic of inverters was studied to be inherent and negative at some frequencies. On this basis, the stability criterion of grid-connected inverters was obtained: in the case that the system impedance has resistance characteristic, if the conductance property of all the grid-connected inverters is positive, the grid-connected system is stable; if there is the inverter with negative damping characteristic, the grid-connected system has the resonance risk. Therefore, an inverter damping control method was proposed. In the premise that the inverter closed-loop is stable, the inverter impedance characteristic curve can be calibrated with the purpose that the inverter conductance is stable positive value in the whole frequency band, so the inverter impedance characteristic can meet the condition of maintaining the system stability. Simulation and physical experiments demonstrated the effectiveness of the analytical method and the control method.