This invention relates to a purifying-catalyst for exhaust gas emitted from internal combustion engines such as automobiles, and the object is to provide a catalyst which exhibits excellent exhaust gas purification performance at lower temperature compared to usual catalysts, even after high temperature aging, and a process for preparation thereof.This object has been attained by an exhaust gas-purifying catalyst containing on a support having a monolithic structure as catalytic components at least one element of the platinum group, activated alumina, cerium, a coprecipitated ceria-stabilized zirconia oxide and optionally a zirconium compound, and a process for preparation of the above exhaust gas-purifying catalyst which comprises(a) preparing activated alumina containing at least one element of the platinum group,(b) preparing a slurry containing this prepared platinum group element-containing activated alumina, cerium oxide, the coprecipitated ceria-stabilized zirconia and optionally the zirconium compound, and(c) coating the slurry onto the support having a monolithic structure and calcining it.