A catalyst (18) is housed in a casing (11) arranged in the exhaust passage (16) of the engine (1). A pressure reducing valve (23), which is usually closed, is arranged in a bypass passage (21) branching off from the exhaust passage (17) upstream of the casing. The fuel injector (8) usually injects fuel at the combustion stroke or the exhaust stroke to feed hydrocarbon, and NOX is reduced in the catalyst by the hydrocarbon. When the catalyst is judged to be poisoned, the timing of the secondary fuel injection is advanced with respect to the timing of the usual secondary fuel injection, and the pressure reducing valve is opened to reduce the pressure in the casing. In this way, the catalyst is reactivated.