Exhaust gas purification system for internal combustion engine

An exhaust gas purification system comprises a NOx catalyst for absorbing the NOx in the exhaust gas when the air-fuel ratio of the influent exhaust gas is lean and purifying by reducing the absorbed NOx with a reducing agent in the exhaust gas when the air-fuel ratio of the exhaust gas turns rich, a first unit for calculating the amount of NOx absorbed per unit time in each area of the NOx catalyst when the air-fuel ratio of the exhaust gas flowing into the NOx catalyst is lean, and a second unit for calculating the total amount of NOx absorbed into the NOx catalyst by totaling the amounts of NOx calculated by the first calculation unit for the areas of the NOx catalyst.