A catalyst for purification of exhaust gas comprising: a promoter compound consisting of a promoter component particle covered with a high heat-resistant oxide ; and a catalytic active species adjacent to the promoter compound ; wherein the promoter component particle is an oxide comprising at least one of Mn, Fe, Ni, Co, Cu and Zn; and the high heat-resistant oxide comprises ZrO 2 and one or more than one species of CeO 2 , Y 2 O 3 , La 2 O 3 , CaO and Nd 2 O 3 ; and wherein the catalytic active species comprises a first metallic oxide , catalytic active particles born on the first metallic oxide and a second porous metallic oxide ; and wherein the catalytic active particle is caged within the second porous metallic oxide so that the catalytic active particle is restrained from being moved, wherein the catalytic active particles comprise at least one precious metal, wherein the precious metal comprises at least one of Pt, Pd, Rh, Au, Ag, Ir and Ru and wherein the first metallic oxide and the second porous metallic oxide comprises at least one of Al 2 O 3 , CeO 2 , ZrO 2 , Y 2 O 3 , La 2 O 3 and Nd 2 O 3 or wherein the promoter component particle is an oxide comprising at least one of Mn, Fe, Ni, Co, Cu and Zn; and the high heat-resistant oxide comprises ZrO 2 and one or more than one species of CeO 2 , Y 2 O 3 , La 2 O 3 , CaO and Nd 2 O 3 ; and wherein the catalytic active species comprises a composite oxide particle and a porous metallic oxide , wherein the composite oxide particle is caged within the porous metallic oxide so that the composite oxide particle is restrained from being moved; wherein the composite oxide particle comprises at least one precious metal and at least one rare-earth element; wherein the precious metal comprises at least one of Pt, Pd, Rh, Au, Ag, Ir and Ru, wherein the rare-earth element comprises at least one of La, Ce, Pr, Nd and Sm and wherein the metallic oxide comprises at least one of Al 2 O 3 , CeO 2 , ZrO 2 , Y 2 O 3 , La 2 O 3 and Nd 2 O 3 . a promoter compound consisting of a promoter component particle covered with a high heat-resistant oxide ; and a catalytic active species adjacent to the promoter compound ; wherein the promoter component particle is an oxide comprising at least one of Mn, Fe, Ni, Co, Cu and Zn; and the high heat-resistant oxide comprises ZrO 2 and one or more than one species of CeO 2 , Y 2 O 3 , La 2 O 3 , CaO and Nd 2 O 3 ; and wherein the catalytic active species comprises a first metallic oxide , catalytic active particles born on the first metallic oxide and a second porous metallic oxide ; and wherein the catalytic active particle is caged within the second porous metallic oxide so that the catalytic active particle is restrained from being moved, wherein the catalytic active particles comprise at least one precious metal, wherein the precious metal comprises at least one of Pt, Pd, Rh, Au, Ag, Ir and Ru and wherein the first metallic oxide and the second porous metallic oxide comprises at least one of Al 2 O 3 , CeO 2 , ZrO 2 , Y 2 O 3 , La 2 O 3 and Nd 2 O 3 or wherein the promoter component particle is an oxide comprising at least one of Mn, Fe, Ni, Co, Cu and Zn; and the high heat-resistant oxide comprises ZrO 2 and one or more than one species of CeO 2 , Y 2 O 3 , La 2 O 3 , CaO and Nd 2 O 3 ; and wherein the catalytic active species comprises a composite oxide particle and a porous metallic oxide , wherein the composite oxide particle is caged within the porous metallic oxide so that the composite oxide particle is restrained from being moved; wherein the composite oxide particle comprises at least one precious metal and at least one rare-earth element; wherein the precious metal comprises at least one of Pt, Pd, Rh, Au, Ag, Ir and Ru, wherein the rare-earth element comprises at least one of La, Ce, Pr, Nd and Sm and wherein the metallic oxide comprises at least one of Al 2 O 3 , CeO 2 , ZrO 2 , Y 2 O 3 , La 2 O 3 and Nd 2 O 3 . <EOS>