A particulate filter arranged in an engine exhaust passage is provided with alternately arranged exhaust gas inflow and outflow passages and porous partition walls separating these passages from each other. In each partition wall, a coated zone where a coated layer with an average pore size smaller than that of a partition wall substrate is used to cover the substrate surface and a non-coated zone downstream of the coated zone where the substrate surface is not covered by the coated layer are defined, and the ash in the exhaust gas can pass through the partition wall in the non-coated zone. The quantity of particulate matter trapped at the non-coated zones is calculated, and PM removal control for removing particulate matter from the particulate filter is performed when it is judged that the quantity of trapped particulate matter is greater than an allowable upper limit amount.