The energy storage system of a pure electric vehicle must meet the requirements of high power density and high energy density at the same time. However, it is difficult for a single energy storage unit to have these two characteristics in the meantime currently. Reasonable hybridization of high energy density lithium batteries and high power density supercapacitors is an effective solution to the problems. This research designs a lithium battery/supercapacitor hybrid energy storage system for the BMW I3 pure electric vehicle and proposes a driving condition-adaptive rule-based energy management strategy for the hybrid energy storage system, which takes into account the requirements of external working conditions and the charging status of battery and supercapacitor. Based on the idea of rapid control prototype, a verification platform for the proposed energy management strategy of the hybrid energy storage system is established with the dSPACE as the control center. The experimental verification of the energy management strategy is completed with an external electric loading equipment which can edit power requirement parameters. The experimental results show that, the hybrid energy storage system equipped with energy management strategy presents good performances on both energy and power densities, better meet the requirements of modern pure electric vehicles for endurance mileage and power performance. At the same time, it can save energy, and may play a role in extending the life cycle of energy storage system.