The disclosure is intended to oxidize PM deposited in a filter in a suitable manner. Provision is made for a filter of wall flow type, a temperature raising unit to raise the temperature of the filter from a downstream side thereof, an exhaust gas shut-off valve, and a controller. The controller controls a flow of exhaust gas in the filter by once fully closing the exhaust gas shut-off valve and then fully opening it when the flow rate of the exhaust gas is equal to or larger than a predetermined flow rate, so as to cause PM to move to a downstream side portion in the filter in the direction of flow of exhaust gas, and carries out regeneration processing which oxidizes the PM by using the temperature raising unit after the controller has caused the PM to move to the downstream side portion of the filter.