Abstract: In this article a new algorithm of surface interpolation over a network of triangles is presented．First of all，it constructs a cubic polynomial interpolating function on each triangle．The integrated surface is smooth．And then，it divides every triangle into 15 sub-triangles．The contour map of the new network of sub-triangles replaces that of the old given network．This method reduces the complexity and quickens the speed very much．The result is satisfactory．