This paper proposes an adaptive low-dc-link-voltage-controlled $LC$ coupling hybrid active power filter ($LC$-HAPF) with a neutral inductor, which can compensate both dynamic reactive power and current harmonics in three-phase four-wire distribution power systems. Due to its adaptive low-dc-link-voltage characteristic, it can obtain the least switching loss and switching noise and the best compensating performances, compared with the conventional fixed and newly adaptive dc-voltage-controlled $LC$-HAPFs. The design procedures of the dc-link voltage controller are discussed, so that the proportional and integral gains can be designed accordingly. Moreover, the general design procedures for the adaptive dc-voltage-controlled $LC$-HAPF with a neutral inductor are also given. The validity and effectiveness of the adaptive dc-link voltage-controlled $LC$ -HAPF with a neutral inductor are confirmed by experimental results obtained from a 220-V 10-kVA laboratory prototype compared with the conventional fixed and adaptive dc-link voltage-controlled $LC$- HAPFs without a neutral inductor.