A method for making epitaxial structure is provided. The method includes providing a substrate having an epitaxial growth surface, patterning the epitaxial growth surface; placing a graphene layer on the patterned epitaxial growth surface, and epitaxially growing an epitaxial layer on the epitaxial growth surface. The graphene layer includes a number of apertures to expose a part of the patterned epitaxial growth surface. The epitaxial layer is grown from the exposed part of the patterned epitaxial growth surface and through the aperture.