It is generally recognized that developing effective methods for selective oxidation of hydrocarbons to generate more useful chemicals is a major challenge for the chemical industry. In the present study, density functional theory calculations are conducted to examine the catalytic partial oxidation of methane (CH4) and ethylene (C2H4) by nitrous oxide (N2O) over Al-incorporated porphyrin-like N-doped graphene (AlN4-Gr). Adsorption energies for the most stable configurations of CH4, C2H4, and N2O molecules over the AlN4-Gr catalyst are determined to be −0.25, −0.64, and −0.40 eV, respectively. According to our findings, N2O can be efficiently split into N2 and Oads species with a negligible activation energy on the AlN4-Gr surface. Meanwhile, CH4 and C2H4 molecules compete for reaction with the activated oxygen atom (Oads) that stays on the surface. The energy barriers for partial methane oxidation through the CH4 + Oads → CH3° + HOads and CH3° + HOads → CH3OH reaction steps are 0.16 eV and 0.27 eV, respectively. Furthermore, the produced CH3OH may be overoxidized by Oads to give formaldehyde and water molecules by overcoming a relatively low activation barrier. The activation barriers for C2H4 epoxidation are small and comparable to those for CH4 oxidation, implying that AlN4-Gr is highly active for both reactions. The high energy barrier for the 1,2-hydrogen shift in the OCH2CH2 intermediate, on the other hand, makes the production of acetaldehyde impossible under normal conditions. According to the population analysis, the AlN4-Gr serves as a strong electron donor to aid in the charge transfer between the Al atom and the Oads moiety, which is necessary for the activation of CH4 and C2H4. The findings of the present study may pave the way for a better understanding of the catalytic oxidation the CH4 and C2H4, as well as for the development of highly efficient noble-metal free catalysts for these reactions.