Fuel cell UAVs have become a research hotspot in green aviation because of their high efficiency, pollution-free emissions and high energy density. Parameter matching of fuel cell hybrid system has an important impact on the economy, environmental protection and efficiency of UAVs. In this study, a vertical take-off and landing fixed-wing UAV was used as a hybrid system of fuel cell + lithium-ion battery. According to the technical indicators, the components of the UAV power system are selected. Firstly, the topology of fuel cell hybrid system is designed, and the parameters of fuel cell (PEMFC), lithium battery, brushless DC motor, propeller and unidirectional DC/DC converter in the hybrid system are matched. Then, the load power is created according to the task profile, and finally the MATLAB/Simulink simulation analysis of the hybrid system is carried out using the finite state machine energy management control strategy. The results show that the designed fuel cell hybrid system can meet the flight load requirements, meet the changes of working conditions during flight, and achieve zero-emission flight.