A systematic approach to the analysis and design of a bi-directional Cuk converter for the cell voltage balancing control of a series-connected lithium-ion battery string is presented in this paper. The proposed individual cell equalizers (ICE) are designed to operate at discontinuous-capacitor-voltage mode (DCVM) to achieve the zero-voltage switching (ZVS) for reducing the switching loss of the bi-directional DC/DC converters. Simulation and experimental results show that the proposed battery equalization scheme can not only enhance the bi-directional battery equalization performance, but also can reduce the switching loss during the equalization period. Two designed examples are demonstrated, the switch power losses are significantly reduced by 52.8% from the MOSFETs and the equalization efficiency can be improved by 68-86.9% using the proposed DCVM ZVS battery equalizer under the specified cell equalization process. The charged/discharged capacity of the lithium-ion battery string is increased by using the proposed ICEs equipped in the battery string.