The negative-sequence current component and harmonic components generated when an asymmetrical fault occurs in the power grid seriously affect the normal operation of the photovoltaic (PV) grid-connected inverter. In order to suppress the negative-sequence current component and the harmonic component of the grid-connected current, and to meet the normal grid-connected operation requirements of the PV grid-connected inverter when asymmetrical faults occur in the grid, this paper proposes the proportional integral double-resonant (PI-DR) current controller, which consists of the PI controller and double-resonant controllers. The PI-DR current controller can directly control the negative-sequence current component and the grid-connected current harmonic component in the output current in the forward synchronous rotating coordinate system, without decomposing the positive and negative sequence currents. The PI-DR current controller ensures that the PV grid-connected inverter can realize normal grid-connected operation and improves the quality of the power when an asymmetrical fault occurs in the power grid. MATLAB/Simulink experiments show that the PI-DR current controller can improve the dynamic characteristics of the PV grid-connected inverter and improve the operating capability of the system when an asymmetrical fault occurs in the power grid.