a catalyst for purifying an exhaust gas includes an upstream side catalyst and a downstream side catalyst . the upstream side catalyst is disposed on an upstream side with respect to an exhaust gas flow , and the downstream side catalyst is disposed on a downstream side with respect thereto . the upstream side catalyst includes a first loading layer , being composed of an alumina containing ba and la at least , and a first noble metal , being held by the first loading layer and being at least one member selected from the group consisting of pd , pd and rh and pd and pt . alternatively , in addition to the aluminum , the first loading layer can be composed of ce , a solid solution of ce and zr and a solid solution of ce , zr and y in an amount as less as possible . the downstream side catalyst includes a second loading layer , being composed of at least one member selected from the group consisting of an alumina containing la , ce , a solid solution of ce and zr and a solid solution of ce , zr and y , and a second noble metal , being held by the second loading layer and being composed of at least one member selected from the group consisting of pt , pd and rh .