In this paper the problem of blending parametric surfaces using subdivision patches is discussed. A new approach, named removing-boundary, is presented to generate piecewise-smooth subdivision surfaces through discarding the outmost quadrilaterals of the open meshes derived by each subdivision step. Then the approach is employed both to blend parametric bicubic B-spline surfaces and to fill n-sided holes. It is easy to produce piecewisesmooth subdivision surfaces with both convex and concave corners on the boundary, and limit surfaces are guaranteed to be C2 continuous on the boundaries except for a few singular points by the removing-boundary approach. Thus the blending method is very efficient and the blending surface generated is of good effect.