The transfer-free synthesis of high-quality, large-area graphene on a given dielectric substrate, which is highly desirable for device applications, remains a significant challenge. In this paper, we report on a simple rapid thermal treatment (RTT) method for the fast and direct growth of high-quality, large-scale monolayer graphene on a SiO2/Si substrate from solid carbon sources. The stack structure of a solid carbon layer/copper film/SiO2 is adopted in the RTT process. The inserted copper film does not only act as an active catalyst for the carbon precursor but also serves as a "filter" that prevents premature carbon dissolution, and thus, contributes to graphene growth on SiO2/Si. The produced graphene exhibits a high carrier mobility of up to 3000 cm(2) V(-1) s(-1) at room temperature and standard half-integer quantum oscillations. Our work provides a promising simple transfer-free approach using solid carbon sources to obtain high-quality graphene for practical applications.