Fuel Cell Hybrid Vehicles (FCHVs) have already become the subject of major interest among automotive industry as well as power management strategies of FCHVs, as the fuel economy of FCHVs depends on them. There are several types of power management strategies of FCHVs that have been developed to improve the fuel economy of FCHVs. Among them, optimal control theory is applied to this study. A problem is defined and its objective is to minimize the energy consumption of an FCHV and to find the optimal trajectories of powertrain parameters during driving. Necessary conditions for the optimal control are introduced and the simulation results of constant costate are compared to that of variable costate in order to prove that the variable costate can be replaced with the constant costate.