An object is to provide technology that enables an NOx catalyst to exercise its NOx reduction capability satisfactorily at any flow speed of the exhaust gas flowing into the NOx catalyst. An exhaust gas purification apparatus for an internal combustion engine includes a selective catalytic reduction NOx catalyst including at least a first catalyst layer having capability of reducing NOx and a second catalyst layer having oxidation capability and arranged closer to a catalyst substrate than the first catalyst layer. The apparatus has a supply valve for adding a specific addition quantity of reducing agent for reducing NOx to inflowing exhaust gas flowing into the selective catalytic reduction NOx catalyst. The apparatus further has a controller that is configured to control addition of the reducing agent by the supply valve based on the flow speed of the inflowing exhaust gas in such a way that the concentration of the reducing agent in a reducing agent atmosphere formed in the inflowing exhaust gas in a reducing agent addition period becomes equal to a specific concentration that is determined based on the flow speed of the inflowing exhaust gas and at which the reducing agent is assumed not to reach the second catalyst layer, when the temperature of the selective catalytic reduction NOx catalyst exceeds a specific temperature at which reduction of NOx by the first catalyst layer is carried out.