Abstract: The grid-connected inverter with LCL filter has the ability of easily attenuating the high frequency current harmonics. However, the effect on the current of the background harmonic voltage and the command signal is difficult to be suppressed. In order to improve the harmonic suppression capability of the output current, a new harmonic damping strategy for single grid-connected inverter was proposed on the basis of analyzing the conventional current tracking control strategy. The influence of the closed-loop parameters on system performance was analyzed and the design of control parameters was presented. Frequency domain analysis, simulation and experimental results show that the proposed control strategy can effectively suppress the effect from background harmonic voltage and the command signal,realizing the control target of high-quality output current.