Single crystals of hexagonal graphenes were successfully grown on Cu foils using the atmospheric pressure chemical vapor deposition (CVD) method. We investigated the effects of reaction parameters, such as the growth temperature and annealing time, on the size, coverage, and density of graphene domains grown over Cu foil. The mean size of the graphene domains increased significantly with increases in both the growth temperature and annealing time, and similar phenomena were observed in graphene domains grown by low pressure CVD over Cu foil. From the comparison of micro Raman spectroscopy in the graphene films grown with different annealing times, we found that the nucleation and growth of the domains were strongly dependent on the annealing time and growth temperature. Therefore, we confirmed that when reaction time was same, the number of layers and the degree of defects in the synthesized graphene films both decreased as the annealing time increased.