To be able to efficiently and rapidly reduce noxious exhaust gas components after starting of an engine without impeding activation of a catalyst device, and moreover to be able to perform rapid separation of noxious exhaust gas components, an adsorption device 5 for adsorbing noxious exhaust gas components is provided downstream of a catalyst device constituting a main mode of operation of exhaust-gas purification, a honeycomb body carrying adsorbent is disposed within the adsorption device, a bypass passage is formed to one side of the honeycomb body, and a switching valve is provided upstream of those components. After engine starting, the switching valve opens, exhaust gas flows in the passage on the honeycomb body side, and HC is adsorbed by the adsorbent. Meanwhile, when exhaust-gas temperature rises and a condition wherein HC separates from the adsorbent is reached, the switching valve is closed, adsorption components which have become high in temperature due to exhaust gas heat separate from an passage between the downstream of this switching valve and the honeycomb body, and are refluxed via reflux passages and to an upstream side of the foregoing catalyst device.