In order to mitigate the power density shortage of current energy storage systems (ESSs) in pure electric vehicles (PEVs or EVs), a hybrid ESS (HESS), which consists of a battery and a supercapacitor, is considered in this research. Due to the use of the two ESSs, an energy management should be carried out for the HESS. An optimal energy management strategy is proposed based on the Pontryagin's minimum principle in this research, which instantaneously distributes the required propulsion power to the two ESSs during the vehicle's propulsion and also instantaneously allocates the regenerative braking energy to the two ESSs during the vehicle's braking. The objective of the proposed energy management strategy is to minimize the electricity usage of the EV and meanwhile to maximize the battery lifetime. A simulation study is conducted for the proposed energy management strategy and also for a rule-based energy management strategy. The simulation results show that the proposed strategy saves electricity compared to the rule-based strategy and the single ESS case for the three typical driving cycles studied in this research. Meantime, the proposed strategy has the effect of prolonging the battery lifetime compared to the other two cases.