Exhaust purifying apparatus of internal combustion engine

An exhaust filter 38 includes a filter for trapping particulate matter contained in exhaust gas and a NOx storage reduction catalyst coated on the filter. As an S release control of the exhaust filter 38, a fuel adding valve 68 intermittently adds fuel to exhaust gas. While fuel is added to exhaust gas, the degree of a temperature increase due to the fuel addition is monitored after the first addition of fuel. Based on the results of monitoring, whether the second and subsequent additions of fuel need to be performed is determined. Accordingly, sulfur oxides occluded by the NOx storage reduction catalyst are adequately reduced.