Although crown gear couplings are widely used in rotating machinery, very little is known about their contact behavior and load distribution characteristics. In this study, the manufacturing methods are presented for crown gear coupling. Complete geometrical mathematical models from tools to crown gear coupling are proposed based on the theories of differential geometry and gear mesh. Then, a high-fidelity finite element model verified by tooth contact analysis under light load is employed to investigate load distribution along the crown gear coupling interfaces. The effects of meshing position, torque, and angular misalignment are investigated on load distributions along with crowning amount depending on the displacement circle radius. Finally, it is observed that when the contact position is 0.2 times the width of the tooth, the radius of the displacement circle is the optimal result for the performance of the crown gear coupling.