A method of multi-objective optimal energy management is proposed to match the APU fuel consumption and the battery state of health (SOH) in the power system of a range-extended electric bus (REEB). Models are established for the calculation of an auxiliary power unit (APU) system fuel consumption and battery SOH loss. The APU fuel consumption and battery SOH are selected as the optimization objectives, and a performance functional of the multi-objective optimization is provided. The dynamic program (DP) algorithm is applied in the control strategy design for solving the multi-objective problem. Under the conditions of the Modified New European Drive Cycle (MNEDC) and Chinese Typical Urban Drive Cycle (CTUDC), which have been used to evaluate the performance of the proposed methodology, the matching-relation between SOH penalty coefficients of battery pack and APU fuel consumption, the SOH of a battery pack can be analysed. Taking the costs of a battery pack and fuel consumption in the whole life cycle as the comprehensive evaluation index, an optimization design method is proposed to match the capacity and the SOH of the battery pack. The simulation results show that when batteries do not need to be replaced, the best economical results will be achieved if the parameters of battery pack and the control strategy parameters are both taken the minimum.