In the field of Fuel Cell Electric Vehicles (FCEVs), a fuel-cell stack usually works together with a battery to improve powertrain performance. In this hybrid-power system, an Energy Management Strategy (EMS) is essential to configure the hybrid-power sources to provide sufficient energy for driving the FCEV in different traffic conditions. The EMS determines the overall performance of the power supply system; accordingly, EMS research has important theoretical significance and application values on the improvement of energy-utilization efficiency and the serviceability of vehicles’ hybrid-power sources. To overcome the deficiency of apparent filtering lag and improve the adaptability of an EMS to different traffic conditions, this paper proposes a novel EMS based on traffic-condition predictions, frequency decoupling and a Fuzzy Inference System (FIS). An Artificial Neural Network (ANN) was designed to predict traffic conditions according to the vehicle’s running parameters; then, a Hull Moving Average (HMA) algorithm, with filter-window width decided by the prediction result, is introduced to split the demanded power and keep low-frequency components in order to meet the load characteristics of the fuel cell; afterward, an FIS was applied to manage power flows of the FCEV’s hybrid-power sources and maintain the State of Change (SoC) of the battery in a predefined range. Finally, an FCEV simulation platform was built with MATLAB/Simulink and comparison simulations were carried out with the standard test cycle of the Worldwide harmonized Light vehicle Test Procedures (WLTPs). Simulation results showed that the proposed EMS could efficiently coordinate the hybrid-power sources and support the FCEV in following the reference speed with negligible control errors and sufficient power supply; the SoC of the battery was also maintained with good adaptability in different driving conditions.