An Al.sub.0.15Ga.sub.0.85N layer 2 is formed on a silicon substrate 1 in a striped or grid pattern. A GaN layer 3 is formed in regions A where the substrate 1 is exposed and in regions B which are defined above the layer 2. At this time, the GaN layer grows epitaxially and three-dimensionally (not only in a vertical direction but also in a lateral direction) on the Al.sub.0.15Ga.sub.0.85N layer 2. Since the GaN layer grows epitaxially in the lateral direction as well, a GaN compound semiconductor having a greatly reduced number of dislocations is obtained in lateral growth regions (regions A where the substrate 1 is exposed).