Graphene, a one-atom-thick layer of carbon with sp2 hybrid orbital bonding and two-dimensional structure material ，has excellent electrical, mechanical, and optical properties. With its extraordinary structure and excellent properties，graphene has great application potential in many fields such as semiconductors, electronics, optics, and sensors. While graphene can be prepared by direct exfoliation from mother materials or growth on transition metals, the uncontrolled production or the additional complex transfer process has been challenging for graphene applications, therefore the direct preparation of graphene on the dielectric substrate by CVD has become an interesting research direction. This paper reviews the research progress of direct preparation of graphene by CVD on dielectric substrates surface at home and abroad, systematically introduces the main methods of direct preparation of graphene on dielectric material surface, and expounds that the catalytic conditions and growth parameters during the growth process are the key to the preparation of graphene on dielectric substrates. In addition, due to the weak catalysis on the surface of dielectric materials, the direct preparation of graphene on the surface has small domain size and poor electrical properties. Therefore, the realization of high quality and controllable preparation of graphene on the surface of dielectric materials is the future research direction.