Previously, the required dc-link voltage of the three-phase four-wire (3P4W) LC- coupling hybrid active power filter (LC-HAPF) was developed based on balanced loading condition. To extend its operation into unbalanced loading cases, this paper presents a general mathematical deduction of the LC-HAPF required dc-link voltage through the circuit models in zero-, positive- and negative-sequence (0-1-2 coordinate). However, a significant high dc-link voltage will be required to compensate both reactive and unbalanced currents when the coupling LC part is designed based on the original method. Thus, the LC-HAPF will lose its key benefit with low dc-link operating voltage, and increasing the system initial cost, switching loss and switching noise. In this paper, a novel coupling LC design method is proposed to effectively reduce the LC-HAPF dc-link voltage, which is based on the considerations in both reactive and unbalanced currents. Finally, representative simulation results of the 3P4W LC-HAPF for reactive and unbalanced currents compensation are given to verify the correctness and effectiveness of the proposed deduced and designed methods.