Molecular dynamics method has been applied to the research on the process of crack propagation of single crystal γ-TiAl. The atomic trajectory figure, energy evolution and the relationship between stress and strain were obtained after the holes size effect had been studied. The results indicate that the initiation stress decreased with holes size increased. After the crack combined with the hole: when R=1?, crack occurred at the center of holes boundary after holes deformation , and it propagated along the direction of [100] until material fracture, mother-child model was found; when R=2?, crack occurred at one corner after holes deformation, and it propagated along the direction of [100] until material fracture; when R=3?, crack occurred at two corners after holes deformation, and it propagated along the direction of [110]and , which mother-child model was found at the direction of [110], and child crack occurred at boundary which combined with crack in this direction and propagate until material fracture. In addition the crack propagate was inhibited by the hole.