An HC adsorbent and a first three-way or oxidation catalyst are installed in an exhaust conduit of an internal combustion engine in that order in a flow direction. A second three-way or oxidation catalyst is installed upstream of the HC adsorbent in the exhaust conduit. When the exhaust gas flows through the second catalyst, the thermal energy of the exhaust gas is compensated for warming-up the second catalyst in a cold period. As a result, the warming-up of the HC adsorbent is delayed and the HC adsorbent can adsorb the HC included in the exhaust gas for a relatively long period. After the second catalyst has been warmed-up, the HC included in the exhaust gas flowing into the HC adsorbent is oxidized. As a result, the HC adsorbent is prevented from being saturated for a short period of time.