This paper presents an algorithm for constructing a smooth interpolation surface on space meshes. The algorithm is a generalization of a radial basis function interpolation surface defined on a quadratic spline surface, which was created using subdivision surface method. That is, a bi-quadratic piecewise Bezier surface is firstly constructed on a space mesh by subdivision surface method, then a radial basis function interpolation surface defined on the spline surface was generated. The algorithm is simple, efficient, and general aesthetically pleasing shapes with the advantage of both interpolation and smoothness.