It is determined quickly whether there is a shortage in reducing agent supplied to an NOx selective reduction catalyst. After it is determined that a quantity of reducing agent equal to or larger than a predetermined quantity is absorbed in the NOx selective reduction catalyst on the assumption that there is no abnormality in reducing agent supply unit, the supply of a quantity of reducing agent needed to reduce a quantity of NOx flowing into the NOx selective reduction catalyst is started. A determination of an abnormality in the reducing agent supply unit is made based on the NOx removal rate after the lapse of a predetermined period of time since the start of the supply of reducing agent. The NOx removal rate becomes lower when there is an abnormality in the reducing agent supply unit.