In this paper, a vector proportional-integral (VPI) current controller for the LC-HAPF with ideally zero steady-state error, optimal transient response and good robustness is proposed. First, the transfer function of the proposed VPI current controller is introduced, and its parameter design for obtaining optimal transient response is discussed. Secondly, a detailed robustness analysis of the VPI current controller including the system parameter variation, distorted grid voltage and grid frequency variation conditions is proposed. Thirdly, the digital implementation method of the VPI controller and an overall control block diagram for the LC-HAPF with the proposed VPI current controller are presented. Moreover, a comparative study and analysis between the VPI current controller and the other representative current controllers under the minimum DC-link voltage is discussed, in which the VPI current controller obtains the best performances under the minimum DC-link voltage operation. Simulation and experimental results are provided to verify the advantages and effectiveness of the proposed VPI current controller for a three-phase four-wire LC-HAPF in comparison with the other representative current controllers under different DC-link voltage conditions. Finally, the robustness under different grid conditions and unbalanced compensation capability of the proposed VPI controlled LC-HAPF is also verified by experimental results.