In this paper, a novel control scheme to mitigate the grid current distortion due to grid voltage disturbance is proposed for a grid-connected voltage-source converter (VSC) with inductor-capacitor-inductor (LCL) filters. Voltage unbalance and harmonics in three-phase systems cause the DC-link voltage ripples and the grid current distortion. In order to mitigate the input current distortion and the DC-link voltage ripples, the multi-loop harmonic current controllers are applied to regulate positive- and negative-sequence currents as well as high-order harmonic currents by proportional-integral (PI) and proportional-resonance (PR) regulators, respectively. In addition, a new active damping method which is the PR controllers regulating the grid current at a resonant frequency is employed to increase the control stability of the VSC with LCL filter. The resonant grid current component is extracted by the band-pass filters (BPF). Furthermore, the positive- and negative-sequence and harmonic components of grid voltages and currents are obtained by a composite observer. The simulation and experimental results have been illustrated to validate the effectiveness of the proposed method.