Aiming at the problem of difficulty in matching the core components of the hybrid power system of amphibious land and air vehicles, this paper proposed a power system matching optimization strategy. Firstly, the components of the hybrid power system, including the engine, the generator, and the power battery pack, were modeled. Secondly, a multi-objective optimization problem was constructed by taking the power performance, fuel economy, and battery health status as the optimization objectives, and taking the number of battery packs and the power of the engine-generator set as the optimization variables. Lastly, a non-dominated sorting genetic algorithm integrating Lévy flight and sine cosine algorithm (LF-SCA-GA) was proposed. The simulation results demonstrate that after power matching, the power performance, fuel economy, and battery health status are enhanced compared with the initial design of the power system.