A methane (CH4) gas is synthesized from carbon dioxide (CO2) and hydrogen (H2) using catalyst-dielectric barrier discharge (DBD) plasma at room temperature and atmospheric pressure. In the method and apparatus for synthesizing methane gas of the invention, methane (CH4) gas, which is synthetic natural gas, can be effectively synthesized only from carbon dioxide (CO2) and hydrogen (H2) using DBD plasma at room temperature and atmospheric pressure, and also, additional heating and pressurization devices are not used during the methane gas synthesis process, thus reducing production costs and realizing high-value-added processing due to the absence of risks during the processing.