Engine exhaust purification device

A controller computes an oxygen storage amount of a catalyst based on the characteristics of an exhaust flowing into the catalyst, and controls the air-fuel ratio of an engine so that the oxygen storage amount of the catalyst is a target value. When it is determined that the engine starts from the warmed-up state when the engine starts, the air-fuel ratio of the engine is controlled to rich until the exhaust flowing out of the catalyst becomes rich. In this way, all the oxygen stored by the catalyst is first released, the NOx purification performance of the catalyst is maintained, and the NOx release amount immediately after engine startup is suppressed.