Fracture parameters of an inclined surface crack in a graded half-plane subjected to sliding frictional contact are investigated in this study. The problem is modelled via the finite element method (FEM) under the plane strain assumption employing a newly developed displacement boundary condition. The shear modulus of the half-plane is graded exponentially through the thickness direction by means of the homogeneous finite element approach. The augmented Lagrange algorithm is selected as an iterative contact solver. The mixed mode stress intensity factors (SIFs) which are induced by the contact stresses are evaluated utilizing the Displacement Correlation Technique (DCT). The accuracy of the present procedure is ensured comparing the SIF results to those calculated by an analytical method for vertical surface cracks. Additional SIF curves are generated as functions of the crack inclination in order to reveal the effects of non-homogeneity, punch location, crack length and friction coefficient. The prominent conclusion of this study indicates that the crack orientation has profound effects on the behavior of Si]' curves, which has not been presented in any study published so far. Hence, consideration of crack inclination is proved essential to successfully predict fracture behavior of a graded medium under frictional contact.