NO and CO are recognized as the major source of air pollution and are expected toward selective catalytic oxidation under different environments. Based on density functional theory (DFT) calculations, the formation configuration and surface activity of metal Co and nonmetal N atoms co-doping graphene (Co-N-3-graphene) as substrate are investigated. Firstly, the adsorption behaviors of gas reactants on Co-N-3-graphene sheet are comparably analyzed. It is found that the coadsorption of OH/NO and OH/CO molecules have the larger adsorption energies than that of the single NO or CO, thus the Langmuir-Hinshelwood (LH) mechanism for NO or CO oxidation reactions will be considered. Secondly, the coadsorption of 2NO molecules is more stable than that of the 2CO and the interaction between 2NO and 2CO molecules through Eley-Rideal (ER) mechanism are also investigated. So, the possible reaction mechanisms for NO or CO oxidation on Co-N 3 -graphene are explored. In the O environments, the formation of HONO or HOCO complex and NO or CO are easily generated NO2 or CO2 with smaller energy barriers (< 0.1 eV), which is an energetically more favorable than the LH and ER mechanisms. These results will provide an important reference for designing high performance graphene-based catalyst for CO or NO oxidation.