The lifetime of fuel cell stacks is a major issue currently, especially for automotive applications. In order to take into account the lifetime of fuel cell stacks while considering the fuel consumption minimization in fuel cell hybrid vehicles (FCHVs), a Pontryagin's Minimum Principle (PMP)-based power management strategy is proposed in this research. This strategy has the effect of prolonging the lifetime of fuel cell stacks. However, there is a tradeoff between the fuel cell stack lifetime and the fuel consumption when this strategy is applied to an FCHV. Verifying the positive economic influence of this strategy is necessary in order to demonstrate its superiority. In this research, the economic influence of the proposed strategy is assessed according to an evaluating cost which is dependent on the fuel cell stack cost, the hydrogen cost, the fuel cell stack lifetime, and the lifetime prolonging impact on the fuel cell stack. Simulation results derived from the proposed power management strategy are also used to evaluate the economic influence. As a result, the positive economic influence of the proposed PMP-based power management strategy is proved for both current and future FCHVs.