To solve the problem of the contact ellipse in the geometric contact simulation of gear teeth which needs the numerical approximation of the quadratic approximation of the tooth surface and the complicated curvature derivation,the method of contact ellipse calculation based on numerical iteration is proposed. Firstly,the instantaneous contact point is solved by meshing basic equations,then the whole week search is conducted according to the given elastic deformation starting from the point,the instantaneous contact ellipse and the long and short axes of the contact position are obtained,and then the whole tooth surface contact prints are got.Finally,taking a pair of cycloidal gear hypoid gears as an example,the feasibility of this method is verified by comparison with commercial software and rolling inspection results.