A catalyst for purifying an exhaust gas includes a support and a noble metal loaded on the support. The support includes a mixture containing a porous oxide and a composite oxide. The composite oxide is expressed by the following formula: (Al 2 O 3 ) a (CeO 2 ) b (ZrO 2 ) 1-b (Y 2 O 3 ) c (La 2 O 3 ) d in which the values "a", "b", "c" and "d" are molar ratios and the value "a" falls in a range of from 0.4 to 2.5, the value "b" falls in a range of from 0.2 to 0.7, the value "c" falls in a range of from 0 to 0.2 and the value "d" falls in a range of from 0 to 0.1. The support includes a particle having a particle diameter of 5 µm or more in an amount of 30% by volume or more. With the thus arranged support, even when the catalyst is subjected to such a severe durability test that it is heated at 1,000 °C for 10 hours, it exhibits a high purifying activity, and its coating layer is inhibited from cracking or coming off.