Abstract: The fatigue of the grid structure with bolt-sphere joints under the function of suspended crane has been greatly concerned by engineers and researchers. The fatigue mainly behaves the fatigue of high strength bolts. ANSYS FEA is provided for studying eight kinds of 40Cr high strength bolts of M14, M20, M24, M30, M33, M39, M52 and M60. According to the quantitative analysis of four principle influencing factors of bolt diameters, screw threads, rounded corner radius of screw thread bottoms and bolt-spheres, a three-dimensional real model is developed by SOLID95 of twenty joints. A calculating formula of fatigue notch coefficients (suitable for all kinds of high strength bolts) has been given. Its data are between 4.35 and 4.89. The results point out that the relation between the stress concentration and fatigue original, which will lay a foundation for fatigue-computational methods of the grid structure with bolt-sphere joints pertinent to hot stresses and the range of hot stresses.