Hybrid Active Power Filter (HAPF) is a combination of Passive Power Filter (PPF) and Active Power Filter (APF). Compare to PPF, HAPF can solve the resonance problem and enlarge the compensation range. Compare to APF, the rating and the cost of HAPF has a great reduction. Therefore, HAPF is a cost-effective and functional power quality compensator. Due to these advantages, the development of HAPF has dramatically increased, and HAPF has been applied into variety power quality applications. Among different circuit topologies of HAPF, the structure of the LC coupling Hybrid Active Power Filter (LC-HAPF) has advantages in power quality compensation, especially for reactive power issue. In this thesis, there are three novel control algorithms being proposed, which can enhance the compensating performance, reduce the switching loss and switching noise of the LC-HAPF, so as to reduce the cost of the compensator. (1) For the harmonic current issues, an adaptive hysteresis band current controller is implemented, the controller adjust the hysteresis band according to the source current THD value. Therefore, the switching frequency and the switching loss of the LC-HAPF can be optimized with an appropriate source current THD value. (2) For the reactive power issue, an adaptive dc-link voltage control method for the LC-HAPF is proposed, in which the dc-link voltage of the active inverter part is varied according to the reactive power consumption of the current loading. (3) To achieve the adaptive dc-link voltage control method, an appropriate dc-link voltage control algorithm is proposed. Under this control algorithm, the dc-link voltage can be controlled as reference one without any pre-charging process as well as not to affect the reactive power compensation. All corresponding operating principles and detail discussions will be given in following chapters. Moreover, simulation and/or experimental results are given to verify the proposed control algorithms can be effectively applied in the LC-HAPF to enhance the compensating performance.