Based on the microstructure change and damage characteristics of single crystal, a two-state-variable crystallographic creep damage constitutive model has been developed to investigate crack growth behaviors of single crystal compact tension specimen at 760 for two crack orientations: (001) and (011). Numerical simulation results show the crack-tip stress fields are dependent on crack crystallographic orientation. Observations performed on the real single crystal specimens reveals that the macroscopic crack growth path appears as zigzag wave. The creep deformation at crack tip takes place in specific slip plane, and the deflection angles of crack initiation direction from the crack plane are 45º or 135 º and 53.7ºor 127.3º in the crack orientations (001) and (011). A good agreement between experimental observations and numerical results is found.