Under real-life driving conditions, hilly roads are prevalent. Hilly road profile substantially influences fuel economy (FE) due to large impacts (increase or decrease) on power demand profile. Thus, the utilization of future altitude profile information has large potential to improve FE. In this paper, for optimal energy management of fuel cell hybrid electric vehicles (FCHEV), we investigate how much FE could potentially be improved when future altitude profile information is available. In particular, the simulation results are analyzed to justify the reason for this potential improvement and to identify which characteristics of hilly roads leads to large FE improvements. First of all, four statistical parameters are defined to characterize hilly roads: mean value, standard deviation (STD), distance interval (DI), and total distance. Then, several types of virtual hilly roads are generated based on various parameter combinations. In order to evaluate the potential FE improvement two energy management strategies (EMSs) are utilized: the first is Dynamic Programming, which evaluates the globally optimal FE when future hilly road information is available; the other is the Equivalent Consumption Minimization Strategy (ECMS) with adaptive equivalent factor for charge-sustenance, which represents the baseline EMS when future hilly road information is not available. The results show that downhill roads have much larger potential than uphill roads do for FE improvements when the future altitude profile is properly used for EMS. Furthermore, if the battery capacity is not large enough to handle the difference in potential energy, future hilly road information is more important to prevent violations of the maximum state-of-charge bound.