Fuel cell hybrid electric vehicles (FCEVs) are mainly electrified by the fuel cell (FC) system. As a supplementary power source, a battery or supercapacitor (SC) is employed (besides the FC) to enhance the power response due to the slow dynamics of the FC. Indeed, the performance of the hybrid power system mainly depends on the required power distribution manner among the sources, which is managed by the energy management strategy (EMS). This paper considers an FCEV based on the proton exchange membrane FC (PEMFC)/battery/SC. The energy management strategy is designed to ensure optimum power distribution between the sources considering hydrogen consumption. Its main objective is to meet the electric motor’s required power with economic hydrogen consumption and better electrical efficiency. The proposed EMS combines the external energy maximization strategy (EEMS) and the bald eagle search algorithm (BES). Simulation tests for the Extra-Urban Driving Cycle (EUDC) and New European Driving Cycle (NEDC) profiles were performed. The test is supposed to be performed in typical conditions t = 25 °C on a flat road without no wind effect. In addition, this strategy was compared with the state machine control strategy, classic PI, and equivalent consumption minimization strategy. In terms of optimization, the proposed approach was compared with the original EEMS, particle swarm optimization (PSO)-based EEMS, and equilibrium optimizer (EO)-based EEMS. The results confirm the ability of the proposed strategy to reduce fuel consumption and enhance system efficiency. This strategy provides 26.36% for NEDC and 11.35% for EUDC fuel-saving and efficiency enhancement by 6.74% for NEDC and 36.19% for EUDC.