Methanation, which synthesizes methane from carbon dioxide and hydrogen, can potentially be an important core technology for realizing a carbon-neutral society. A catalyst is normally used in the methanation process, but its thermal degradation is a serious problem. Thus, we have proposed a catalyst-free methanation reactor that simulates an internal combustion engine. We call it a Methanation Reciprocating Engine (MeRE), where the up-and-down motion of the piston inside the engine creates a high-temperature, high-pressure field inside the reactor that is suitable for the methanation reaction. In this study, we conducted a 0-dimensional simulation using a program package, Chemkin-II. To make clear the reactor characteristics based on the reaction process in the MeRE, we used an ICEN code (Internal Combustion Engine) to simulate the MeRE. We changed the initial temperature, the components of reactants, the rotational speed, and the compression ratio. It is found that the reaction rate of methane production can be enlarged by increasing the initial temperature, the compression ratio, and the rotational speed. Additionally, it is better to set the composition which is close to the stoichiometric ratio of the Sabatier reaction. For all cases, the CO2 conversion rate is high, but the CH4 selectivity is very low. Resultantly, in the case of the MeRE, it is easy to produce CO from CO2, while the reaction which converts from CO to CH4 is unlikely to take place.