Fuel cell electric vehicles are widely deemed as the promising technology in sustainable transportation field, yet the high ownership cost makes them far from competitive in contemporary auto market. To maximize the economic potential of fuel cell/battery-based hybrid electric vehicles, this paper proposes a real-time cost-minimization energy management strategy to mitigate the vehicle’s operating cost. Specifically, the proposed strategy is realized via model predictive control, wherein both hydrogen consumption and energy source degradations are incorporated in the multi-objective cost function. Assisted by the forecasted speed, dynamic programming is leveraged to derive the optimal power-splitting decision over each receding horizon. Thereafter, the performance discrepancy of the proposed strategy is analyzed under different affecting factors, including battery state-of-charge regulation coefficient, discrete resolution of optimization solver, speed prediction approaches and length of prediction horizon. Lastly, a comparative study is conducted to validate the effectiveness of the proposed strategy, where the proposed strategy can respectively reduce the operating cost and prolong the fuel cell lifetime by 14.17% and 8.48% in average versus a rule-based benchmark. Moreover, the online computation time per step of the proposed strategy is averaged at 266.26 ms, less than the sampling time interval 1 s, thereby verifying its real-time practicality.