To produce active sites with high activity which can not be obtained with a single oxide by using a mixed oxide containing aluminum and one or more transition metal elements and partly substituting aluminum atom of aluminum oxide with the transition metals.

This waste gas purifying catalyst is a mixed oxide containing aluminum and one or more elements selected from cobalt, nickel, and copper with which aluminum of aluminum oxide is partly substituted. Since a large number of active sites with high activity which can not be obtained with only a single oxide are formed by substituting specified sites of the oxide containing aluminum as a main component with the transition metal element, and the obtained catalyst is highly active. In this case, as the oxide containing aluminum as a main component, pure aluminum oxide having Al2O3 composition and variously modified type aluminum oxides to which various additives are added may be used.