The spherical gear is a new gear-driven mechanism with a double degree of freedom. Based on the mathematical models of spherical gears, the meshing model is obtained and tooth contact analysis is performed, so the location of contact points on teeth surfaces is received by using nonlinear solver. The structural shape of the tooth surface is studied. To the point contact form of meshing spherical gears between a convexity and a saddle surface, contact ellipses of meshing tooth surfaces are studied, and then the movement rule of contact ellipses when spherical gear pairs mesh in any swaying plane that passes through polar axes of spherical gear pairs is gained: Contact ellipses are little on teeth base and teeth tip, so contact stress is large; Contact ellipses are relatively large on teeth mid-position, so contact stress is little. Finite element analysis is applied to perform bending stress analysis and tooth contact stress analysis, and the result validates the correctness of the movement rule of contact ellipses. The study is useful for further investigations in transmission theory and practical applications of spherical gear pairs.