A method for purifying an exhaust gas characterized in that a catalyst for purifying an exhaust gas, comprising a support including rutile titania, a NOx storage material including at least one element selected from the group consisting of alkali metals, alkaline-earth metals and rare-earth elements and loaded on the support, and a noble metal loaded on the support, is disposed in an exhaust gas of an oxygen-rich atmosphere made by burning an air-fuel mixture whose air-fuel ratio, A/F (air/fuel), is 18 or more, so that NOx in the exhaust gas are stored in the NOx storage material, and whose air-fuel ratio is varied from the stoichiometric point to a fuel-rich atmosphere periodically so that the NOx stored in the NOx storage material are released, thereby carrying out reducing and purifying, wherein at least part of said rutile titania and said NOx storage material forms a composite oxide.