Using the improved element-free Galerkin (IEFG) method, in this paper we introduce the characteristic parameter r which can reflect the singular stress near the crack tip into the basic function of the improved moving least-squares (IMLS) approximation. Combining fracture theory with the IEFG method, we present an IEFG method of treating the elastic fracture problems, and analyze a numerical example of two-dimensional layered system of airport composite pavement with reflective crack. In the IEFG method, the IMLS approximation is used to form the shape function. The IMLS approximation is presented from the moving least-squares (MLS) approximation, which is the basis of the element-free Galerkin (EFG) method. Compared with the MLS approximation, the IMLS approximation uses the orthonormal basis functions to obtain the shape function, which leads to the fact that the matrices for obtaining the undetermined coefficients are diagonal. Then the IMLS approximation can obtain the solutions of the undetermined coefficients directly without the inverse matrices. The IMLS approximation can overcome the disadvantages of the MLS approximation, in which the ill-conditional or singular matrices are formed sometimes. And it can also improve the computational efficiency of the MLS approximation. Because of the advantages of the IMLS approximation, the IEFG method has greater computational efficiency than the EFG method which is based on the MLS approximation, and can obtain the solution for arbitrary node distribution, even though the EFG method cannot obtain the solution due to the ill-conditional or singular matrices in the MLS approximation. Paving the asphalt concrete layer on the cement concrete pavement is an effective approach to improving the structure and service performance of an airport pavement, which is called airport composite pavement. The airport composite pavement has the advantages of rigid pavement and flexible pavement, but there are various forms of joints or cracks of cement concrete slab, which makes the crack reflect into the asphalt overlay easily under the plane load and environmental factors. Reflective crack is one of the main failure forms of the airport composite pavement. Therefore, it is of great theoretical significance and engineering application to study the generation and development mechanism of reflective crack of the airport composite pavement. For the numerical methods of solving the fracture problems, introducing the characteristic parameter r which can reflect the singular stress near the crack tip into the basic function is a general approach. In this paper, we use this approach to obtain the IEFG method for fracture problems, and the layered system of airport composite pavement with reflective crack is considered. The numerical results of the displacements and stresses in the airport composite pavement are given. And at the tip of the crack, the stress is singular, which makes the crack of the airport composite pavement grow. This paper provides a new method for solving the reflective crack problem of airport composite pavement.