Many problems are associated with the large battery operation current, such as battery overheating, lithium plating, and mechanical structural instability of battery materials. All these problems may cause battery safety issues in fuel cell hybrid vehicles (FCHVs), e.g., battery explosions and thermal runaway have been reported and may cause public anxiety about FCHVs. Previous researches on FCHV power management strategy have focused on minimizing fuel consumption. But more attention needs to put on the battery current constraint for analysis of battery state of charge (SOC) and battery state of health (SOH). This research targets optimizing the FCHV battery pack operation within a safe current range through power management strategy to increase the safety of the battery pack while improving battery usage via SOC control. Battery SOH is also evaluated in the study. This paper presents a Pontryagin's minimum principle (PMP)-based FCHV power management with consideration of battery current constraint, SOC, and SOH. PMP is applied as the power management strategy to optimize splitting the power between battery pack and fuel cell stack at each time step during the operation. Battery current constraint is coupled as a cost function in PMP control with fuel consumption as another cost function. The results show that applying battery current constraint results in a smaller battery current range and two times less of the SOC drop slope. In addition, 0.02% of battery SOH improvement is obtained under one single FTP-72 driving cycle.