The micro crack propagation process and the fracture propagation mechanism of the single crystal γ-TiAl alloy of different crystallographic orientation on the microstructure has been studied. The prefabricated micro crack propagation process was simulated of three different crack crystallographic orientations of [100]、[110]and[111] for the single crystal γ-TiAl alloy by the molecular dynamics method. It showed that: The crack stress value is the minimum of [100] crystal orientation, and the crack intensity is the lowest so that it is easy to extend in the form of brittle cleavage extension. The stress has always focused on the crack tip in the process of the extension,and the system of stress decreasesed with time increased,The crack stress value of the [111] orientation is the largest. And the larger the crack strength, the more difficult to extend. The crack propagation process showed the obvious orientation effect. The micro crack extended by the way of crack tip slip dislocation and twin slip was formed on the crack tip. The stress distribution mainly focused on the crack tip and twinning plane in the process of extension, and decreased with time increased. The crack stress value of [110] orientation between two other crystallographic orientations,The Early extension is brittle cleavage extension and the crack tip atoms into chaos after expanded to a certain time and after the crack tip launch dislocation makes the crack tip passivation .As load continued, one the end of passivation crack tip sharp again and sub crack initiation which is not a flat surface with the main crack. At last,the main crack and the sub crack connected to form the micro cracks of step extension. The extension process showed some effect of orientation. The stress always focused on the crack tip, and decreased with time increased. The different crystallographic orientation has great influence to the micro crack propagation.