The advance of CVD technique to directly grow graphene on the insulating substrates is particularly significant for further device fabrication. As graphene is catalytically grown on metal foils, the degradation of the sample properties is unavoidable during transfer of graphene on the dielectric layer. Moreover, shortening the treatment time as possible, while achieving single-layer growth of graphene, is worthy to be investigated for promoting the efficiency of mass production. Here we performed a rapid heating/cooling process to grow graphene films directly on the insulating substrates by thermal CVD. The treating time consumed is approximate to 25% compared to conventional CVD procedure. In addition, we found that high-quality, single-layer graphene can be formed on quartz, but on SiO2/Si substrate only few-layer graphene can be obtained. The pronounced substrate effect is attributed to the different dewetting behavior of Ni films on the both substrates at 950 degrees C. (C) 2015 Elsevier B.V. All rights reserved.