An approach of blending edges and venices of a polyhedron with NURBS surfaces that are C' continuous along their common boundaries is presented in this paper. In general, the edge blending is a bit easier, but the vertex blending is more difficult. The approach presented in this paper can unify the transaction of these two cases. Compared with other method presented, first, NURBS surface can represent the edge blending surface (constant radius blending or variable radius blending) precisely; second, In blending the vertex, they depart the blending surfaces of its adjacent edges, so they don't need to meet with each other, then "supplementary surfaces" are generated to make C' transitions between them. They generate the blending surfaces by constructing boundary curve networks with C' continuity, then according to the continuity rule, generating the NURBS surfaces.