Dynamic meshing of Spiral bevel gears is a complicated geometric, material, and contact non-linear problem. The finite element method (FEM) is a common and effective approach and direct constraint method is highly advantageous to solve contact non-linear problems. In this paper, a three-dimensional nonlinear contact analysis model for a pair of spiral bevel gears was established. Based on this model, dynamic meshing simulation under 200rpm and 462.1N•m of torque was carried out in a meshing period. The regular pattern indicating variety of tooth surface contact stress and tooth root bending stress with different meshing position was presented. Then this paper analyzed the contact fatigue and root bending fatigue strength, estimated the major region of fatigue, and finally obtained the least tooth root bending fatigue lifetime. The results will act as a reference for further design of spiral bevel gears.