A lean NOx trap type exhaust gas purifying catalyst having a catalyst noble metal selected from a group consisting of platinum, palladium and rhodium, an inorganic oxide that carries the catalyst noble metal, and at least one NOx adsorbent one selected from a group of magnesium, barium, sodium, potassium and cesium. The inorganic oxide carrying palladium containing cerium in a CeO2-equivalent quantity in a range of 1 to 20 wt %, and at least one of aluminum and zirconium.