We report high-quality GaN crystal grown directly on graphene layers without a buffer layer by metal-organic chemical vapor deposition. Photoluminescence and Raman spectra reveal that GaN crystal grown on graphene layers has mild strain compared to that grown on sapphire and SiO2 substrate. Etch pit was not observed on the surface of GaN/graphene where the threading dislocations were diminished inside the bulk, which is markedly different from GaN/sapphire with threading dislocations present on GaN surface. This opens a new possibility that graphene with pi electron and hexagonal symmetry could be an ideal substrate for GaN crystal growth, instead of using expensive sapphire substrate.