In this paper, the real joint load transfer efficiency of airport pavement is calculated by combining the results of airport pavement deflection detection and ground-penetrating radar detection. Spring elements are used to simulate the actual load transfer efficiency of joints in ABAQUS. The impact of different asphalt overlays on the stress state of the critical point in the pavement is analyzed by the airport cement concrete pavement model. The result shows that adding a thin stress-absorbing layer with fine-graded and low modulus can effectively disperse the load transferred from the asphalt pavement to the cement pavement and the stress concentration at the joint under the asphalt overlay. Compared with airport pavement without a stress-absorbing layer, the tensile stress and shear stress at the critical point in the airport pavement asphalt overlay decreased by 24.62% and 22.49%, respectively. Therefore, the combination of the high-modulus upper layer and low-modulus lower layer can effectively reduce the tensile stress and shear stress at the critical point. In addition, increases in the thickness of the asphalt overlay can effectively improve the stress state at the critical point. When the thickness of the asphalt overlay changed from 13 cm to 21 cm, the maximum tensile and shear stress decreased by 8.82% and 8.92%, respectively. Finally, based on the analysis of the numerical simulation and field test verification, the optimal airport pavement asphalt overlay scheme is proposed.