In an engine which includes an oxidation catalyst and an SCR catalyst in an exhaust passage, a first flow regulating control in which a control valve is controlled so as to decrease a flow rate of an exhaust gas which passes through the oxidation catalyst and the SCR catalyst is performed in a case where the oxidation catalyst is in a low temperature state at the time of performing deceleration fuel cut, and a second flow regulating control in which the control valve is controlled so as to increase the flow rate of the exhaust gas which passes through the oxidation catalyst and the SCR catalyst is performed in a case where the oxidation catalyst is in a temperature state higher than the low temperature state and the SCR catalyst is in a low temperature state at the time of performing the deceleration fuel cut.