The safety of the airport runway, as an infrastructure, is of considerable concern. The existing research has problems of hysteresis and unreasonable load application. In this paper, ANSYS is used to construct a coupled tire–pavement model to study the dynamic characteristics of airport asphalt pavements under impact loading. Taking the Boeing 737–800 as an example, the impact of an aircraft landing on an airport pavement is simulated by applying a dynamic load to the landing gear. The effects of tire pressure, landing pitch angle, and sinking speed on the dynamic response of the airport runway are investigated. The effects of each factor of the airport pavement are analyzed by comparing the maximum effective stress, effective strain, and displacement in the vertical direction at the same position of different structures. The results show that when the tire pressure is 2.0 MPa, the maximum values of effective stress, effective strain, and vertical displacement increase by 29.8%, 19.1%, and 22.2%, respectively, compared with 1.0 MPa. The maximum values of effective stress, effective strain, and vertical displacement at the 3.0 m/s sinking speed increase by 25.2%, 93.1%, and 77.1%, respectively, compared with that at the sinking speed of 1 m/s, which indicates that the effect of sinking speed on the dynamic response of the pavement is more significant. However, the change in the landing pitch angle has little impact on the response parameters of the pavement. Meanwhile, the flexural tensile stress at the bottom of the surface and the equivalent effect at the top of the soil foundation must be considered in the design of the airport pavement structure.