The mixed finite element algorithm is used to solve contact problems coupling with friction decided by velocity for curved surface in elastic field. The computational procedure is designed with the aid of Fortran language, and the technique is employed to account for the contact problems of one pair of meshing teeth in the plane stress and quasi static situation. The result indicates that the influence of velocity on friction affects the distribution of contact force as well as the meshing node pair’s contact status, and the consideration of the relation between velocity and friction is essential for the contact problem solutions. Ultimately the example is validated by the Ansys software.