TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Components: The zirconia layer has an average thickness of 3-30 mu m. The zirconia layer is formed from a raw material having a particle size of 5 mu m or less. The substrate comprises alpha -alumina. The substrate has a network structure having 5-40 cells per inch. The catalyst support layer comprises an oxide of at least one alkaline earth metal comprising magnesium, calcium, strontium or barium. The catalyst support layer comprises a first component, a second component and a third component, where the first component is an oxide of at least one alkaline earth metal, which is magnesium, calcium, strontium or barium; the second component is an oxide of at least one element, which is scandium, yttrium or lanthanoid; and the third component is zirconia or a solid electrolyte substance mainly composed of zirconia. The zirconia layer consists of at least one of zirconia, calcia-stabilized zirconia, magnesia-stabilized zirconia, yttria-stabilized zirconia and ceria-stabilized zirconia. EXAMPLE - A disc-shaped alpha -alumina foam having an outer diameter of 16 mm and a thickness of 5 mm was prepared as a porous substrate. Yttrium oxide-stabilized zirconium oxide (as a raw material for forming a zirconia layer) was wet-milled to a particle size of 1.0 mu m or less in a ball mill for 24 hours. The procedures of dipping the substrate in slurry (40 wt.%) of the raw material of the zirconia layer, pulling up the substrate, and drying the substrate were performed many times to form an yttrium oxide-stabilized green film on the substrate. The substrate was then calcined at 1400 degrees C in air for 2 hours to form a zirconia layer on the substrate. A sintered compound consisting of catalyst carrier components having a weight ratio of yttrium oxide:zirconia layer:magnesium oxide of 1:1:1 was milled to prepare slurry (40%) for forming a catalyst support layer. The slurry was coated on the zirconia layer in the same manner as described above to form a green film of the catalyst carrier components on the zirconia layer. The substrate having the zirconia layer and the green film was calcined at 1320 degrees C in air for 2 hours to form a catalyst carrier.