The turbo-electric drive compressor with exhaust energy recovery function is the development trend of high-power fuel cell air management system. However, the turbo-electric drive compressor has problems such as low pressure ratio and low energy recovery rate under off-design conditions. In this paper, a high-power fuel cell system was taken as the research object. According to the intake and exhaust parameters of the stack, the three-dimensional aerodynamic design of the turbine expander and the compressor was completed. An electrochemical-flow heat transfer one-dimensional coupling model including the fuel cell stack and the turbo-electric drive compressor was established. The accuracy of the model was verified by the stack test data. Based on this model, the influence of turbine flow characteristics and valve adjustment methods on the exhaust energy recovery rate under full operating conditions was further studied. The results show that under the condition of small and medium load, the exhaust energy recovery rate increases by 5.26 percentage points for every 0.1 reduction of turbine flow coefficient. However, small flow coefficient will cause high stack pressure at the design point, so it is necessary to increase the pressure relief of bypass valve, which leads to the high complexity of the system and big exhaust energy loss. When the turbine flow coefficient is 1, a better energy recovery rate can be obtained under all working conditions. In addition, the valve preposition scheme is better than the postposition scheme, and the valve preposition can increase the energy recovery rate by 6.25% under off-design conditions. Combined with the scheme of turbine flow coefficient of 1 and valve preposition, the exhaust energy recovery rate of the turbo-electric drive compressor is 33.07% and 27.31% respectively at the design flow point and 50% design flow point.