A control unit for an internal combustion engine can activate a three-way catalyst at the early stage and can lessen the deterioration of the exhaust in an internal combustion engine such as HC, CO, and NOx, etc. from the exhaust gas when starting. The control unit for an internal combustion engine is provided with the three-way catalyst and HC adsorbent on an exhaust side. The control unit alternately controls the A/F between a rich state and a lean state in order to quicken the activation of the three-way catalyst when the internal combustion engine starts.