The purpose of this study is to predict the behavior of fatigue crack propagation as one of fracture mechanics on the compressive residual stress. We got the following characteristics from fatigue crack growth test carried out in the environment of room temperature and low temperature at $25^{circ}C$, -6$0^{circ}C$, -8$0^{circ}C$, and -10$0^{circ}C$ in the range of stress ratio of 0.3 by means of opening mode displacement. There is a difference between shot peened specimen and unpeened specimen. Fatigue crack growth rate of shot peened specimen was lower than that of unpeened specimen. Shot peening is improve the resistance of crack growth by fatigue that make a compressive residual stress on surface. That is the constrained force about plasticity deformation was strengthened by resultant stress, which resulted from plasticity deformation and compressive residual stress in the process of fatigue crack propagation. Temperature goes down, fatigue crack growth rate decreased.