This study analyzes the mathematical relationship between DC-link voltage and system parameters for shunt active power filters (APFs). Analysis and mathematical deduction are used to determine the required minimum DC-link voltage for APF. A novel adaptive DC-link voltage controller for the three-phase four-wire shunt APF is then proposed. In this controller, the DC-link voltage reference value will be maintained at the required minimum voltage level. Therefore, power consumption and switching loss will effectively decrease. The DC-link voltage can also adaptively yield different DC-link voltage levels based on different harmonic currents and grid voltage levels and thus avoid the effects of harmonic current and grid voltage fluctuation on compensation performance. Finally, representative simulation and experimental results in a three-phase four-wire center-split shunt APF are presented to verify the validity and effectiveness of the minimum DC-link voltage design and the proposed adaptive DC-link voltage controller.