Abstract: In this work, the effects of N-doping into the Co-doped single vacancy (Co-SV-G) and di-vacancy graphene flake (Co-dV-G) are investigated and compared toward direct oxidation of methane to methanol (DOMM) employing two different oxidants (N2O and O-2) using density functional theory (DFT) calculation. We found that DOMM on CoN3-G utilizing the N2O molecule as oxygen-donor proceeds via a two-step reaction with low activation energies. In addition, we found that although CoN3-G might be a good catalyst for methane conversion, it can also catalyze the oxidation of methanol to CO2 and H2O due to the required low activation barriers. Moreover, the adsorption behaviors of CHx (x = 0-4) species and dehydrogenation of CHx (x = 1-4) species on CoN3-G are investigated. We concluded that CoN3-G can be used as an efficient catalyst for DOMM and N-2O reduction at ambient conditions which may serve as a guide for fabricating effective C/N catalysts in energy-related devices.