In an engine, a controller is configured to fully close the opening of EGR valve when a cut condition is satisfied and variably control the opening when a cut release condition is satisfied. An operating zone is defined as a zone surrounded by a characteristic curve indicating a relationship between rotation speed and torque. The operating zone comprises a high operating zone containing an NTE zone, and a low operating zone that is set at a lower torque side and at a lower rotation speed side with respect to the high operating zone. The cut condition is that an operating condition specified by the rotation speed and the torque is kept within the low operating zone during a predetermined time or more. The cut release condition is that the operating condition falls within the high operating zone.