With the synthesis of graphene on Cu using CVD, it was tried to show the behavior of graphene growth depending on the size and orientation of Cu grain. It was found out that even under the same temperature and pressure the use of different gases influences on the diffusion rate of Cu. As compared to Ar gas, Cu grain growing bigger under $H_2$ and $CH_4$ was resulted in bigger graphene grain. Corrosion resistance was evaluated by potentiodynamic polarization test in room temperature and found out that the graphene on Cu was more stable in order of 10 than pure Cu due to the chemical stability of graphene. The future work of this research will focus on the synthesis of graphene having no defects including grain boundaries, and its engineering use.