Graphyne is of great interest to researchers due to its unique electronic and mechanical properties, which make it a potentially valuable material for a wide range of applications. The importance of graphyne lies in its potential to enable new technologies and applications in a variety of fields, from electronics to materials science. In this paper, the density functional theory (DFT) calculation was used to investigate CO2 and N2 adsorption on pristine and oxidized γ-graphyne in both two horizontal and vertical directions at hollow and bridge sites. Based on the results, the highest stability was observed when the CO2 and N2 molecules approached the γ-graphyne sheet in a hollow space. Oxygenation of γ-graphyne led to increased CO2 adsorption capacity compared to pristine γ-graphyne. This can be attributed to the interaction between the Pπ electrons of the carbon in graphyne and carbonyl groups with the unbonded electron pair of the oxygen in CO2, leading to a more significant interaction of CO2 with the γ-graphyne surface. Furthermore, no significant N2 absorption was observed for oxygenated γ-graphyne.