In order to enhance the fuel economy performance of the new-generation propeller aircraft, a power management method for serial hybrid-electric propulsion system is designed and analyzed. First, a mathematical model of the serial hybrid-electric propulsion system was established under aircraft/engine integrated framework. In addition, the performance matching of the propeller aircraft and the serial hybrid-electric propulsion system was accomplished through reverse design method. Subsequently, power management strategies were devised based on the fixed and variable turbine speeds to minimize fuel consumption of the turboprop engine and accomplish the optimal power allocation between turboprop engine and lithium battery. Finally, performance parameters variation laws of the serial hybrid-electric propulsion system under different power management methods were revealed and compared. The results demonstrate that, in the case of a consistent flight profile, the power management method based on variable turbine speed can dramatically decrease the total fuel consumption by more than 2.28%, thereby providing a substantial advantage in obtaining superior fuel economy. Furthermore, it is noteworthy that under identical flight mission phase, the optimal power turbine speeds corresponding to different cruising altitudes remain approximately constant. This observation highlights the superiority and feasibility of the power management method of the serial hybrid-electric propulsion system.