Energy management strategies (EMSs) directly affect the fuel economy of hybrid electric vehicles, and deep reinforcement learning (DRL) has become the mainstream method for energy management in recent years. This paper proposes an intelligent DRL-based EMS for an urban fuel cell bus (FCB) powered by both fuel cell and battery to improve the energy efficiency of the FCB. To begin, an enhanced soft actor-critic (SAC) algorithm integrating the standard SAC algorithm with the prioritized experience replay (PER) mechanism is innovatively formulated. Then, an intelligent EMS based on the enhanced SAC algorithm is developed. After that, the superiority of the proposed EMS is evaluated in detail by comprehensive comparisons. Simulation results indicate that the proposed EMS accelerates the convergence speed by 62.79% while improving the fuel economy by 5.18% in comparison with the EMS based on standard SAC.