The growth process of graphene structure on 6H-ＳiC（0001） surface has been studied using the classical molecular dynamics （MD） simulation and the simulated annealing technique. We show that carbon atoms of the 6H-ＳiC（0001） subsurface after sublimation of Si atoms can be self-organized to form local monolayer graphene structures. This process is similar to the formation of graphene on the 6H-ＳiC（0001） surface, depending strongly on annealing temperature and coverage of carbon atoms on the SiC（0001）surface. The local graphene structures can be formed on 6H-ＳiC（0001）as the annealing temperature is around 1400 K. This transformation temperature is in good agreement with experimental observations （1080 ℃）, but is lower than that of growing graphene on SiC（0001） surface （T≈1450　K）. In addition, not only single layer but also bilayer graphene structure can be formed, associated with the increase of the coverage of carbon atoms on SiC（0001）surface.