In this paper, molecular dynamics is used to simulate the self-assembly of carbon atoms and the growth of graphene on the surface of cemented carbide, which has some advantages, such as reducing manufacturing costs, shortening the experimental cycle, and optimizing the preparation parameters of graphene. A proper potential function is designed to simulate the formation of graphene on the WC (10 \bar1 0) surface and Co (0001) surface by a single carbon atom. The growth process of graphene, such as the deposition of carbon atoms, the formation of carbon chains with different lengths, the transformation about carbon chains into polygons, and the basic units and natural defects of graphene are investigated in detail. Three processes of self-repair of graphene defects, including carbon chain rotation, splitting and embedding, are described respectively. The effects of temperature and carbon deposition rate on the growth of high-quality graphene are also studied. The simulation results show that at low temperature, the mobility of carbon atoms is low and grown graphene contains a lot of defects, and the coverage of the substrate is low, which leads to low quality graphene to be prepared. High temperature promotes the migration of carbon atoms and helps to grow high quality graphene. However, high temperature can cause damage to the substrate and reduce the flatness of the growing graphene. At a higher deposition rate, the nucleation rate of graphene is higher and the distribution is more uniform. However, due to the different ability of each graphene nucleus to absorb carbon atoms, there are many macrocyclic defects in the graphene. The low deposition rate has a longer annealing time, which excessively stimulates the migration of carbon atoms. It leads to the aggregation of carbon atoms and reduce the quality of graphene. The proper deposition rate can ensure the nucleation density of graphene, and at the same time, it has enough time to form six membered rings and repair defects, which is conducive to the formation of the high quality graphene. Therefore, it is significantly important to design the appropriate deposition temperature and deposition rate for the growth of high-quality graphene. After optimizing the simulation parameters, high-quality graphene is successfully grown at 1300 K deposition temperature and 10 ps/C deposition rate.