A composite strategy is proposed to address the optimal power management for a hybrid powered compound-wing aircraft, which integrates bang–bang regulation with optimal demand chasing regulation. The electro-gasoline hybrid power system enhances the overall flight endurance of vertical take-off and landing compound-wing aircraft. The power consumption in level flight appears to be much lower than that in hovering, enabling the hybrid power system to simultaneously energize and charge the battery pack. In order to minimize fuel consumption and battery pack degradation during level cruise flight, a power management strategy that serves for both battery charging and thrust energizing is worthy of careful consideration. To obtain the desired features and design the regularity strategy of the power system, linear and nonlinear models are established based on the configuration of an electro-gasoline series hybrid power system installed in the proposed aircraft, with mathematical modelling of key components and units. A notable feature of semi-fixing for battery voltage and engine rotational speed has been qualitatively identified and subsequently quantitatively validated on the testbench. After conducting simulations and comparing with other strategies, the composite strategy demonstrates appropriate fuel consumption and battery degradation, effectively achieving cost minimization. Testbench evaluation confirms the effectiveness of this proposed power management strategy. Furthermore, the practicality of the hybrid power system and its associated level flight composite power management strategy are validated by tests conducted on a 30 kg aircraft prototype, thereby showcasing the potential to enhance flight performance.