An exhaust gas purifying catalyst comprises a hydrocarbon adsorbent layer and a metal-based catalyst layer on a monolithic support. The catalyst contains zeolite in the underlying hydrocarbon adsorbent layer and contains noble metals such as palladium, platinum, rhodium, etc. in the overlying metal-based catalyst layer. Also, both layers contain an alkaline metal, etc., and a weight ratio of the alkaline metal, etc. contained in the metal-based catalyst layer to the alkaline metal, etc. contained in the hydrocarbon adsorbent layer is set to 60:40 to 99:1. A process for preparing the above catalyst comprises forming the metal-based catalyst by coating slurry. The slurry contains water insoluble or water hardly-soluble alkaline metal and/or alkaline earth metal compound.