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Graphene layers have been grown on C-terminated 6H-SiC (000-1) substrate by thermal decomposition with the assistance of carbon flux in a solid carbon source molecular beam epitaxy system. Results indicate that the graphene films prepared directly by the reduction of SiC in vacuum chamber are defective and disorder, while appropriate carbon flux added during the graphene growth will favor the graphene layer growth and improve the graphene layer quality. While on the other hand, too much carbon flux will affect the graphene formation and deteriorate the final graphene layer. This carbon flux assisted graphene growth behavior on SiC crystal indicates that the external carbon flux should play an important role for the graphene layer growth during the thermal reduction of SiC in vacuum condition. The mechanism of the graphene layer formed on C-face SiC and the effect of the carbon flux were discussed based on the experimental results.