An engine cooling device includes: a water pump pressure-feeding a common coolant to plural coolant circulation paths; an engine including an engine main body; a water-cooled header cooling an exhaust system of the engine by use of the coolant, a heat capacity of the water-cooled header being smaller than that of the engine main body; an ECU and a thermostat determining whether or not the coolant is allowed to flow through the fifth and sixth coolant circulation paths among the plural coolant circulation paths on the basis of a given determination value. The given determination value relates to an amount of heat transferred from the exhaust gas to the water-cooled header.