GaN system compound semiconductor and method for growing a crystal thereof, which can significantly reduce a concentration of crystalline defects caused by lattice mismatch by growing a GaN system compound semiconductor of GaN or InxGa1-xN by using InxAl1-xN crystal on a substrate as an intermediate buffer layer, the method including the steps of (1) providing a sapphire substrate, (2) growing an intermediate buffer layer of InxAl1-xN on the sapphire substrate, and (3) growing GaN or InxGa1-xN system compound semiconductor on the intermediate buffer layer.