A NOx storing catalyst (11) comprising a precious metal catalyst (46) and NOx absorbent (47) is arranged in an exhaust passage. When the air-fuel ratio of the exhaust gas is lean, the storing catalyst cold stores the NO2 contained in the exhaust in the absorbent when the catalyst is inactive and hot stores the cold stored NO2 in the absorbent when the catalyst is made active. The NO2 contained in the exhaust is cold stored in the absorbent when the catalyst is not activated, and when a predetermined NOx storing catalyst restoring condition (107) is met, a NOx storing catalyst restoring control (109, 115) including raising the NOx storing catalyst temperature to a predetermined temperature to active it (109) is executed so as to restore the cold storing capability of the NOx absorbent.