A cooling apparatus of an exhaust gas recirculation system includes a first cooling portion, made of a first material, that receives recirculation exhaust gas; and a second cooling portion, made of a second, different material, that receives the recirculation exhaust gas from the first cooling portion and exhausts the recirculation exhaust gas out of the apparatus. A cooling method of an exhaust gas recirculation system includes receiving a recirculation exhaust gas in a first cooling portion made of a first material; cooling the recirculation exhaust gas in the first coolant portion; receiving the recirculation exhaust gas in a second cooling portion made of a second, different material; and cooling the recirculation exhaust gas in the second coolant portion.