Thermal decomposition of silicon carbide is a promising approach for the fabrication of graphene. However, the atomistic growth mechanism of graphene remains unclear. This paper describes the development of a new charge-transfer interatomic potential. Carbon bonds with a wide variety of characteristics can be reproduced by the proposed vectorized bond-order term. A large-scale thermal decomposition simulation enables us to observe the continuous growth process of the multiring carbon structure. The annealing simulation reveals the atomistic process by which the multiring carbon structure is transformed to flat graphene involving only six-membered rings. Also, it is found that the surface atoms of the silicon carbide substrate enhance the homogeneous graphene formation.