A filter is made with heat-insulating ceramic fibers, and where the filter is increased in pressure loss due to particulate matter captured after filtration of exhaust gas, gas flow is blocked, a heating element is used to heat the surface of the filter, thereby burning and removing particulate matter. The filter is of heat insulating properties, by which a heat insulating material is arranged near the particulate matter capturing face of the filter, and the heating element is incorporated between the surface of the filter and the heat insulating material. The filter can be regenerated at a higher heating efficiency in a smaller quantity of thermal energy. The heat insulating material is also used as a filter, by which the apparatus can be made more compact. A charging element is arranged upstream of the filter material, by which the filter material is increased in particulate matter capturing performance, thereby suppressing the rate of increase in the pressure loss and improving heating efficiency of particulate matter.