The amount of generation of heat per unit time due to combustion reaction of particulate matter is suppressed, and is made lower than the amount of heat radiation per unit time. By doing so, an abrupt temperature rise called "ignition" is prevented, and a temperature gradient in a filter is made small, thereby preventing unduly-high temperatures from developing. Therefore, the cracking of the filter as well as damage of the filter due to melting can be perfectly prevented, thereby enhancing the reliability. To achieve this, the whole of the filter is heated in such a manner that a temperature rise rate is not more than 10.degree. C./minute when the temperature in the filter is in the range of between 400.degree. C. and 600.degree. C. In the case where the filter carries an oxidizing catalyst, the heating is effected in such a manner that the temperature rise rate is not more than 10.degree. C./minute in the range of between 200.degree. C. and 400.degree. C.