Compared to preparation on metal substrates, graphene synthesis on non-metal surfaces is highly desirable to avoid the deleterious metallic effects in fabrication of electronic devices. However, study of graphene growth mechanism on non-metal surfaces is rare and little understood. Here, we report that few-layers graphene films can be grown directly on silicon-on-insulator surface. Furthermore, the graphene growth mechanism on non-metal surfaces is proposed as a surface reaction, adsorption, decomposition, and accumulation process.