Abstract: The extended finite element method (XFEM) is a new numerical method for modeling both strong and weak discontinuities within a standard finite element framework. In the XFEM, the contact conditions must be considered when the crack faces are closed. The iterative methods were used to solve the nonlinear contact problem in existing researches. In this paper, a linear complementary model for closed frictional crack problems with the XFEM is presented, so that the nonlinear frictional contact between the crack faces is solved with the linear complementary model, thus, the iterative procedure is avoided. Numerical simulations illustrate that the method can effectively model the contact problem, and the combination of the XFEM and linear complementary method has practical merits for solving contact problem.