In a method for manufacturing a high-quality GaN-based semiconductor layer on a substrate of different material, an AlN nucleation layer is grown on a substrate, a GaN buffer layer is grown on the AlN nucleation layer, and the substrate annealed. The AlN nucleation layer is formed to have a thickness greater than a critical radius of a nucleus of AlN crystal and less than a critical resilient thickness of AlN, and the GaN buffer layer is formed to have a thickness greater than a critical radius of a nucleus of GaN crystal and less than a critical resilient thickness of GaN. Annealing time is greater than L2/DGa where L indicates a diffusion distance of Ga, and DGa indicates a diffusion coefficient of Ga in the AlN nucleation layer.