On a substrate made of e.g., sapphire single crystal is formed an Al underlayer having FWHM X-ray rocking curve value of 90 seconds or below. A buffer layer is formed on the AlN underlayer and has a composition of Al.sub.pGa.sub.qIn.sub.1-p-qN (0.ltoreq.p.ltoreq.1, 0.ltoreq.y.ltoreq.q). A GaN-based semiconductor layer group is formed on the buffer layer.