Graphene was obtained on Cu foil by thermal decomposition method. A gas mixture of $H_2$ and $CH_4$ and an ambient annealing temperature of $1,000^{circ}C$ were used during the deposition for 30 Min., and for the transfer onto $SiO_2/Si$ and Si substrates. The physical properties of graphene were investigated with regard to the effect ofnitrogen atom doping and the various substrates used. The G/2D ratio decreased when the graphene became monolayer graphene. The graphene grown on $SiO_2/Si$ substrate showed a low intensity of the G/2D ratio, because the polarity of the $SiO_2$ layer improved the quality of graphene. The intensity of the G/2D ratio of graphene doped with nitrogen atoms increased with the doping time. The quality of graphene depended on the concentration of the nitrogen doping and chemical properties of substrates. High-quality monolayer graphene was obtained with a low G/2D ratio. The increase in the intensity of the G/2D ratios corresponded to a blue shift in the 2D peaks.