An electronic control unit estimates progress of growth in a particle diameter of an ash accumulated in a diesel particulate filter (a DPF), based on an operating state of an engine. If it is determined that an estimated particle diameter of the ash achieved through the progress of the growth is greater than a predetermined value, regeneration of the DPF is compulsorily performed even when a quantity of particulate matters accumulated in the DPF is lower than a reference value, at which the DPF should be regenerated. Thus, the particulate matters are eliminated through combustion, and the ashes are discharged from the DPF.