Control device and method of internal combustion engine

A control device of an internal combustion engine (1) which is equipped with an exhaust system including an exhaust purification device (11) purifying exhaust gas, and which performs a recovery process for recovering purification capability of the exhaust purification device (11) in operation, is provided with a first means (S3, S4) for determining a state of performing the recovery process, a second means (S1, S2) for determining a stop demand for stopping the internal combustion engine (S1, S2), and a third means (S3, S4) for delaying the stop of the internal combustion engine (1) based on the stop demand according to result of the determination of the first means (S3, S4).