(i) In a ceramic catalyst body which comprises a ceramic carrier which has a multitude of pores capable of supporting a catalyst directly on the surface of a substrate ceramic and a catalyst supported on the ceramic carrier, a layer containing an anti-evaporation metal such as Rh is formed on the outer surface of catalyst metal particles such as Pt or Rh. The layer containing the anti-evaporation metal protects the catalyst metal and prevents evaporation thereof, thereby suppressing the deterioration; and/or(ii) A ceramic catalyst body is made by having a main catalyst component and a promoter component directly on a ceramic carrier which can directly support the catalyst by substituting a part of the constituent elements of cordierite, and a trap layer is provided in the upstream thereof for trapping sulfur which is a catalyst poisoning component included in the exhaust gas. Since sulfur included in the exhaust gas can be collected by the trap layer, the catalyst poisoning component can be removed from the gas which enters the catalyst, thus preventing catalyst poisoning.