The selection and parameter of external tooth crowning curve have important influence on the meshing characteristic of the crown gear coupling,which determines the maximum allowable inter-axial angle and meshing performance of the crown gear coupling. The four types of crowning curves of circular,elliptic,hyperbolic and three-segment circular arcs are established by using geometric analysis,the minimum clearance,the contact position,the maximum inter-axial inclination and the contact ratio between the internal and external tooth surfaces at different inclination angles are calculated. The meshing characteristics of four crowning curves are compared. The results show that when the mid-point curvature radius of each crowning curve change respectively in the range of 50 ,90 mm and 90 ,130 mm,the corresponding maximum allowable inter-axis angle decreases by 0. 2° and 0. 1° for every 20 mm increase of curvature radius,the three-section arc curve allows the largest inter-axial angle and the smallest axial displacement at the corresponding maximum allowable inter-axis angle. When the inter-axial angle is greater than 1. 3° and the curvature radius of the intermediate position is the same,the three-section arc corresponds to the tooth surface normal minimum clearance curve is obviously more gentle,meshing coincidence degree is higher.