Numerical simulations are conducted at atmospheric pressure in order to understand the effect of the oxygen enrichment level on structure of $CH_4/O_2/N_2$ premixed flames. Under several equivalence ratios the flame speeds are calculated and compared with those obtained from the experiments, the results of which are in good agreement. The effects of the oxygen enrichment are investigated on flames under fuel-rich conditions. As the oxygen enrichment level is increased from 0.21 to 1, the flame speed and the temperature are increased. The emission index of $CO_2$ is decreased in cases of flames for fuel rich mixtures, so the efficiency of combustion may be decreased. The maximum emission index of NO is obtained for 0.6 of the oxygen enrichment level.