The fuel economy of a fuel cell hybrid vehicle (FCHV) depends on its power management strategy because the strategy determines the power split between the power sources. Several types of power management strategies have been developed to improve the fuel economy of FCHVs. This paper proposes an optimal control scheme based on the Minimum Principle. This optimal control provides the necessary optimality conditions that minimize the fuel consumption and optimize the power distribution between the fuel cell system (FCS) and the battery during driving. In this optimal control, the final battery state of charge (SOC) and the fuel consumption have an approximately proportional relationship. This relationship is expressed by a linear line, and this line is defined as the optimal line in this research. The optimal lines for different vehicle masses and different driving cycles are obtained and compared. This research presents a new method of fuel economy evaluation. The fuel economy of other power management strategies can be evaluated based on the optimal lines. A rule-based power management strategy is introduced, and its fuel economy is evaluated by the optimal line.