The adsorption of carbon dioxide on graphene sheets was theoretically investigated using density functional theory (DFT) and MP2 calculations. Geometric parameters and adsorption energies were computed at various levels of theory. The $CO_2$ chemisorption energies on graphene-$C_{40}$ assuming high pressure are predicted to be 71.2-72.1 kcal/mol for the lactone systems depending on various C-O orientations at the UCAM-B3LYP level of theory. Physisorption energies of $CO_2$ on graphene were predicted to be 2.1 and 3.3 kcal/mol, respectively, at the single-point $UMP2/6-31G^{**}$ level of theory for perpendicular and parallel orientations.