Abstract: To simulate fracture problems that might occur during the engineering service of functionally graded material (FGM) and calculate the corresponding crack initiation loads, graded extended finite element was embedded into ABAQUS software by user-defined subroutine UEL, and physical fields in functionally graded materials were simulated by finite element method. Mixed-mode stress intensity factors (SIFs) were calculated by interactive energy integral post-processing subroutine. Maximum hoop stress criterion was adopted in subroutines to calculate crack deflection angles, and to predict crack propagation paths and crack initiation loads in functionally graded materials were both predicted. Influences of material gradient parameters on cracking propagation paths and crack initiation loads were discussed. The improvement of fracture characteristics in graded composites was validated by comparing with homogeneous materials. The results show that the initial crack perpendicular to the gradient direction tends to propagate towards the part exhibiting lower equivalent elastic modulus, and the crack deflection angle peaks at linear gradient index, and increases with the elastic modulus ratio of constitutes. When the applied load and the initial crack are both parallel to the gradient direction, an increase in the equivalent elastic modulus and fracture toughness or a decrease in the gradient index all lead to an enhanced crack initiation load.