A method for making an epitaxial structure includes the following steps. A substrate having an epitaxial growth surface is provided. A buffer layer is formed on the epitaxial growth surface. A carbon nanotube layer is placed on the buffer layer. A first epitaxial layer is epitaxially grown on the buffer layer. The substrate and the buffer layer are removed to expose a second epitaxial growth surface. A second epitaxial layer is epitaxially grown on the second epitaxial growth surface.