This composite oxide powder can secure a large pore volume even after calcination at high temperature and, when a catalyst is formed by loading a noble metal on this composite oxide powder, noble metal grain growth can be suppressed. The composite oxide powder comprises particles of an oxide of a metal M₁ and an oxide of a metal M₂ which does not dissolve in the oxide of the metal M₁, the oxide of the metal M₁ and the oxide of the metal M₂ being dispersed at the nanometer level. Since different oxides serve as a barrier to each other, sintering is suppressed. Therefore, in the case of composite oxide powder comprising Ce as a metal M₁ and Al as a metal M₂, grain growth is small even after exposed to high temperature and pores of 3.5-100 nm secure a volume of 0.07 cc/g or more after calcination at 600 C. for 5 hours and a volume of 0.04 cc/g or more after calcination at 800 C. for 5 hours.