Monolayer graphene is a two dimensional electron gas (2DEG) which is obtained at room temperature. The optical, electrical and magnetic transport properties (e.g., room temperature quantum Hall effect, high mobility, high thermal conductivity, minimum conductivity, etc.) in graphene represent different transport behaviors for the difference of it′s linear dispersion relation and that of traditional 2DEG. This graphene material has huge potential applications in microelectronics and transparent conductive films. The dielectric function under the random phase approximation (RPA) is employed to evaluate the optical conductivity in the traditional 2DEG and the graphene system. It is found that the main optical conductivity is induced by the inter-band transition with two-branch energy spectrum, while the contribution by the intra-band transition is very small. The shape of the conductivity spectrum depends on the Fermi energy and the broadening width which is determined by the scattering mechanism. When the optical energy is larger than 2EF, the optical conductivity tends to a constant which is consistent with the experimental result.