A method for manufacturing a semiconductor device includes the steps of: (a) preparing a non-polar single crystal substrate; (b) epitaxially growing an MgO layer on the non-polar single crystal substrate to a thickness of 3 nm or thicker to have rocksalt structure at a substrate temperature of 500.degree. C. to 800.degree. C.; (c) growing on the MgO layer a low temperature growth layer made of ZnO group material at a substrate temperature of 500.degree. C. or lower; (d) annealing the low temperature growth layer above the substrate at a temperature of 700.degree. C. or higher; and (e) epitaxially growing a high temperature growth layer of ZnO group material on the annealed low temperature growth layer at a temperature of 600.degree. C. or higher.