The present invention is intended to provide a technique of improving exhaust emissions at the time of starting up of an internal combustion engine, without decreasing the performance of a catalyst at the time of the engine starting up. The present invention is provided with the catalyst that is arranged in an exhaust passage of the internal combustion engine in which a plurality of kinds of fuels are able to be used, and serves to adsorb and remove exhaust gas components discharged from the internal combustion engine, wherein in cases where among the plurality of kinds of fuels, a first fuel is used in which unburnt fuel components thereof are easily adsorbed to the catalyst, at the time when a request is made for stopping the internal combustion engine, said first fuel is changed to a second fuel thereby to operate said internal combustion engine until said internal combustion engine is stopped.