This paper presents a new Fuel Cell Fuel Consumption Minimization Strategy (FCFCMS) for Hybrid Electric Vehicles (HEVs) powered by a fuel cell and an energy storage system, in order to minimize as much as possible the consumption of hydrogen while maintaining the State Of Charge (SOC) of the battery. Compared to existing Energy Management Strategies (EMSs) (such as the well-known State Machine Strategy (SMC), Fuzzy Logic Control (FLC), Frequency Decoupling and FLC (FDFLC), and the Equivalent Consumption Minimization Strategy (ECMS)), the proposed strategy increases the overall vehicle energy efficiency and, therefore, minimizes the total hydrogen consumption while respecting the constraints of each energy and power element. A model of a hybrid vehicle has been built using the TruckMaker/MATLAB software. Using the Urban Dynamometer Driving Schedule (UDDS), which includes several stops and accelerations, the performance of the proposed strategy has been compared with these different approaches (SMC, FLC, FDFLC, and ECMS) through several simulations