The direct growth of graphene on insulating substrates presents significant promise for the advancement of next-generation semiconductor technologies. Here, the synthesis of graphene directly on sapphire substrates via chemical vapor deposition (CVD) is reported. The CVD growth parameters are systematically manipulated to optimize the crystal quality of graphene. Furthermore, the dependency of graphene growth on the crystallographic orientation of the sapphire substrate is explored to elucidate the underlying mechanisms. It is found that robust C-O chemical bonds are established between the oxygen atoms on the sapphire surface and the carbon atoms in the graphene, predominantly influencing the nucleation process. The oxygen-rich nature of the c-plane sapphire surface contributes to a higher graphene nucleation density and the formation of smaller grains comparing to r-plane sapphire. Accordingly, high quality and uniform monolayer graphene is successfully obtained on both c-plane and r-plane sapphire.