High-quality monolayer graphene was synthesized on high-kappa dielectric single crystal SrTiO3 (STO) substrates by a facile metal-catalyst-free chemical vapor deposition process. The as-grown graphene sample was suitable for fabricating a high performance field-effect transistor (FET), followed by a far lower operation voltage compared to that of a SiO2-gated FET and carrier motilities of approximately 870-1050 cm(2).V-1.s(-1) I in air at rt. The directly grown high-quality graphene on STO makes it a perfect candidate for designing transfer-free, energy-saving, and batch production of FET arrays.