This paper aims at obtaining the mathematical model of the general spiral bevel gears of local bearing contact from spatial conjugate curve theory. Differential geometry and gearing kinematics are introduced to derive this model. Meshing-correctly conditions are set in the theoretical derivation process. The final model is represented in the form of equations and inequalities. According to the arguments in this paper, a process of designing the tooth surface of spiral bevel gears of local bearing is proposed. Based on this process, the numerical example of a pair of these gears with specific profiles is represented by applying the finite element analysis. Results show that the magnitudes of the deviations between theoretical contact points and real contact points are small. Therefore, the results agree with the mathematical model of the spiral bevel gears of local bearing contact in this paper.