This paper presents an energy management strategy for a hybrid electric propulsion system designed for unmanned aerial vehicles. The proposed method combines the Equivalent Consumption Minimization Strategy (ECMS) and fuzzy logic control, thereby being named Fuzzy based ECMS (F-ECMS). F-ECMS can solve the issue that the conventional ECMS cannot sustain the battery state-of-charge for on-line applications. Furthermore, F-ECMS considers the aircraft safety and guarantees the aircraft landing using the remaining electrical energy if the engine fails. The main contribution of the paper is to solve the deficiencies of ECMS and take into consideration the aircraft safely landing, by implementing F-ECMS. Compared with the combustion propulsion system, the hybrid propulsion system with F-ECMS at least reduces 11% fuel consumption for designed flight missions. The advantages of F-ECMS are further investigated by comparison with the conventional ECMS, dynamic programming and adaptive ECMS. In contrast with ECMS and dynamic programming, F-ECMS can accomplish a balance between sustaining the battery state-of-charge and electric energy consumption. F-ECMS is also superior to the adaptive ECMS because there are less fuel consumption and lower computational cost.