An exhaust gas purifying system and a catalyst used for the system prevents NOx absorbent from being poisoned by a sulfur compound to keep NOx absorption performance. The catalyst has at least an inner and an outer layer on a support material, the inner layer having NOx absorbent capable of absorbing NOx and a sulfur compound in the exhaust gas produced from combustion of a lean fuel mixture, releasing the NOx into the exhaust gas and substantially stopping absorbing the sulfur compound when a rich mixture is burnt, and the outer layer having a sulfur compound absorbent capable of absorbing the sulfur compound in the exhaust gas produced from combustion of a lean fuel mixture and capable of discharging the sulfur compound into the exhaust gas when a rich fuel mixture is burnt while the engine operates in a lean-burn zone. NOx is absorbed by the NOx absorbent in the inner layer and the sulfur compound is adsorbed in the sulfur compound absorbent in the outer layer. Therefor the NOx absorbent in the inner layer is protected from being poisoned by the sulfur compound.