A numerical study was conducted to have the effect of $CO_2$ addition to fuel on the chemical reaction mechanism with the change of the initial concentration of $CO_2$ and the axial velocity gradient. From this study, it was found that there were two serious effects of $CO_2$ addition on a non-premixed flame ; a diluent effect by the reactive species reduction and chemical effect of the breakdown of $CO_2$ by the third-body collision and thermal dissociation. Especially, the chemical effect was serious at the lower velocity gradient of the axial flow. It was certain that the mole fraction profile of $CO_2$ was deflected and CO was increased with the initial concentration of $CO_2$. It was also ascertained that the breakdown of $CO_2$ would cause the increasing of CO mole fraction at the reaction region. It was also found that the addition of $CO_2$ did not alter the basic skeleton of $H_2-O_2$ reaction mechanism, but contributed to the formation and destruction of hydrocarbon products such as HCO. The conversion of CO was also suppressed and $CO_2$ played a role of a dilution in the reaction zone at the higher axial velocity gradient.