To provide a palladium-containing catalyst improved in the catalytic activity of palladium and therefore markedly improved in an HC cleaning performance.

The catalyst is characterized in that Ce and Pd are supported in their atomic states on alumina. Alternatively, the catalyst is one prepared by alumina to carry Ce and Pd, wherein Ce is contained in an amount of 0.1-10 mass% based on the total mass of alumina, Ce, and Pd, and the molar ratio Ce/Pd is 0.04-4, desirably Ce is contained in an amount of 0.5-5 mass% based on the total mass of alumina, Ce, and Pd, and the molar ratio Ce/Pd is 0.2-3. Such catalysts are used to clean an exhaust gas from an internal combustion engine and can exhibit a heightened HC cleaning performance.