The conversion reaction of methane and carbon dioxide at an atmospheric pressure plasma reactor filled with Ni-$Al_2O_3$ and Ni-$MgAl_2O_4$ catalyst was performed. Effects of various process parameters such as the applied electric power, reaction gas flow rate, reactor temperature, mixing ratio of reactants and the presence of the catalyst on the reaction between methane and carbon dioxide were analyzed. From the analysis of the contribution of the catalyst in the reaction step, even if the temperature raised to $400^{circ}C$, there was no spontaneous catalytic conversion of methane and carbon dioxide without plasma discharges. When the catalysts for the conversion of methane and carbon dioxide would be adopted to the plasma reactor, the careful selection of suitable catalysts and process parameters should be essential.