A control device is provided for an engine equipped with an electric oil pump for circulating coolant, and having a flow rate of the coolant restricted, when a temperature of the coolant is lower than a threshold value, as compared to a case where the temperature of the coolant is equal to or higher than the threshold value, and the engine control device includes a coolant temperature sensor detecting a temperature of the coolant, and a control unit stopping the engine in accordance with the temperature to be detected by the coolant temperature sensor after the pump is driven so as to increase the flow rate of the coolant, in a case where the flow rate of the coolant is restricted.