Abstract: We propose a method that needn’t modify subdivision rules for using symmetric strip-shaped mesh to generate Loop subdivision surfaces with curve interpolation constraints.The symmetric strip-shaped mesh is constructed by designing symmetric triangles for both sides of the control polygon of interpolated curve.This control polygon is referred as central polygon.We can prove that the symmetric strip-shaped mesh can converge to the interpolated curve.So the limited surface of the given mesh with the symmetric strip-shaped mesh will contain interpolated curve.If the interpolated curves intersect at point v,we can design a full symmetric triangle mesh at point v.The method proposed in this paper will interpolate intersecting curves in the given mesh.The numbers of intersecting curves are up to six.