A control device includes an electronic control unit. During deceleration of the engine, when a temperature of a three-way catalyst is equal to or higher than a predetermined temperature and execution conditions of fuel cut processing are established, the electronic control unit executes first control for closing an exhaust shutoff valve, while fuel injection and ignition are continued. When the exhaust shutoff valve reaches the closed state in the first control, the electronic control unit executes second control for bringing the engine into an intake control state in which the intake throttle is closed and an EGR valve is in a predetermined open state. In the second control, the electronic control unit executes the fuel cut processing by stopping the ignition before the engine is brought into the intake control state and stopping the fuel injection after the engine is brought into the intake control state.
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