Energy management is an enabling technology for increasing the economy of fuel cell/battery hybrid electric vehicles. Existing efforts mostly focus on optimization of a certain control objective (e.g., hydrogen consumption), without sufficiently considering the implications for on-board power sources degradation. To address this deficiency, this article proposes a cost-optimal, predictive energy management strategy, with an explicit consciousness of degradation of both fuel cell and battery systems. Specifically, we contribute two main points to the relevant literature, with the purpose of distinguishing our study from existing ones. First, a model predictive control framework, for the first time, is established to minimize the total running cost of a fuel cell/battery hybrid electric bus, inclusive of hydrogen cost and costs caused by fuel cell and battery degradation. The efficacy of this framework is evaluated, accounting for various sizes of prediction horizon and prediction uncertainties. Second, the effects of driving and pricing scenarios on the optimized vehicular economy are explored.