Supercharger is widely used in vehicle engines because of its good response characteristics while the application in aircraft piston engines is still very rare. The working process of the supercharger was analyzed, and the linear relationship between the opening and closing pressure of the bypass valve and the turbocharger pressure ratio is modeled on the basis of the reed valve model. The GTPOWER numerical simulation model of a certain type of aero piston engine was established and confirmed. Based on the whole model, the mass flow rate of the bypass valve and the flow area of the bypass valve at different heights were studied. The results show that under the cruise condition, the valve is closed at 2680m above sea level, and the valve is closed at 3000m above sea level under taking off condition which confirm the accuracy of the model provides the theoretical basis for the actual high altitude flight of the engine