Compared with traditional active power filter (APF), the dc-link voltage of LC-coupling hybrid active power filter (LC-HAPF) is lower, thus reducing the system cost and power loss. In order to improve the compensation performance of the LC-HAPF, many current controllers have been proposed in recent decade, which are hysteresis current control (HCC), quasi-proportional-resonant control (QPRC), deadbeat current control (DBCC), second-order sliding-mode control (SOSMC), vector proportional-integral current control (VPIC) and improved model predictive control (IMPC). In this paper, the model of these six controllers will be first reviewed and introduced. After that, their corresponding parameters design methodology are given. Finally, simulation results will be given to compare their compensation performance and summarize their characteristics.