The Energy Management Strategy (EMS) in Fuel Cell Hybrid Electric Vehicles (FCHEVs) is the key part to enhance optimal power distribution. Indeed, the most recent works are focusing on optimizing hydrogen consumption, without taking into consideration the degradation of embedded energy sources. In order to overcome this lack of knowledge, this paper describes a new health-conscious EMS algorithm based on Model Predictive Control (MPC), which aims to minimize the battery degradation to extend its lifetime. In this proposed algorithm, the health-conscious EMS is normalized in order to address its multi-objective optimization. Then, weighting factors are assigned in the objective function to minimize the selected criteria. Compared to most EMSs based on optimization techniques, this proposed approach does not require any information about the speed profile, which allows it to be used for real-time control of FCHEV. The achieved simulation results show that the proposed approach reduces the economic cost up to 50% for some speed profile, keeping the battery pack in a safe range and significantly reducing energy sources degradation. The proposed health-conscious EMS has been validated experimentally and its online operation ability clearly highlighted on a PEMFC delivery postal vehicle.