Numerical simulations of freely propagating fuel-rich $CH_4/CH_3Cl$ premixed flames were performed at atmospheric pressure in order to understand the effect of the oxygen enrichment on the production of PAH. A chemical kinetic mechanism was used, which involved 157 gas-phase species and 1693 forward reactions. The calculated flame speeds were compared with the experiments for the flames established on the equivalence ratios of 1~1.6, the results of which were in good agreement. As the level of oxygen enrichment was increased, the concentrations of one or four ring aromatic hydrocarbons were decreased. This might cause the fact that the contribution of PAH species to soot was weakened.