There is broad interest in surface functionalization of 2D materials and its related applications. In this work, we present a novel graphene layer transistor fabricated by introducing fluorinated graphene (fluorographene), one of the thinnest 2D insulator, as the gate dielectric material. For the first time, the dielectric properties of fluorographene, including its dielectric constant, frequency dispersion, breakdown electric field and thermal stability, were comprehensively investigated. We found that fluorographene with extremely thin thickness (5 nm) can sustain high resistance at temperature up to 400 °C. The measured breakdown electric field is higher than 10 MV cm(-1), which is the heightest value for dielectric materials in this thickness. Moreover, a proof-of-concept methodology, one-step fluorination of 10-layered graphene, is readily to obtain the fluorographene/graphene heterostructures, where the top-gated transistor based on this structure exhibits an average carrier mobility above 760 cm(2)/Vs, higher than that obtained when SiO₂ and GO were used as gate dielectric materials. The demonstrated fluorographene shows excellent dielectric properties with fast and scalable processing, providing a universal applications for the integration of versatile nano-electronic devices.