To enhance the accuracy of the mathematical models during the acceleration and deceleration phases of aircraft engines, this paper presents a component-level identification modeling method based on system identification theory. This approach assumes that each component of the aircraft engine operates as a Hammerstein system, introducing the concept of “component-level identification.” Using this model, the paper simulates the acceleration and deceleration processes of aircraft engines and compares the model predictions with actual operational data. Moreover, additional data from various operational conditions were employed to confirm the wide-ranging applicability of this identification model. The results indicate that this method is effective for constructing mathematical models of aircraft engines and can accurately describe the dynamic linear and static nonlinear characteristics of each engine component. Based on this model, the identification results for key parameters show an average relative error of less than 4% compared to actual data.