An exhaust gas purifying catalyst formed by having a first rhodium-containing catalyst layer, a second zeolite-containing catalyst layer, and a third palladium-containing catalyst layer superposed sequentially on a carrier, and a process for purifying the exhaust gas from an internal combustion engine by using the catalyst. A catalyst possessing durability and excelling in the ability to adsorb hydrocarbon, the ability to purify, and the three-way performance is provided.