Numerical simulations of freely propagating flames burning stoichiometric CH$_4$/O$_2$/$N_2$mixtures are performed at atmospheric pressure in order to understand the effect of the $O_2$enrichment level on CH$_4$/Air flame. A chemical kinetic mechanism is employed, the adopted scheme involving 54 gas-phase species and 632 forward reactions. The calculated flame speeds are compared with the experiments for the flames established at several $O_2$enrichment level, the results of which is in excellent agreement. As a result of the increased $O_2$enrichment level from 0.21 to 1, the mole fraction of CO in the burred gas is increased. The flame speed and the temperature in the burned gas are also increased, but the thickness of the flame is severely shrunken in the preheat region. The maximum of the calculated EINO is obtained around 0.6 and 0.7 of the $O_2$enrichment level in cases of flames for fuel-lean mixtures.