An engine stop control device is provided for a vehicle that ensures a sufficient operation frequency of coast stop operation during travel on a congested road, thereby to improve practical fuel economy. The vehicle has an engine that is capable of being restarted. A controller is configured to stop the engine automatically when the vehicle, after experiencing a travel with a vehicle speed VSP exceeding a first threshold value, decreases the speed below a CS (coast stop) start vehicle speed. The controller is further configured to set a second threshold value below the first threshold value. The controller is further configured, after starting from an engine automatic stop due to the coast stop control and when the vehicle experiences travel exceeding the second threshold value without exceeding the first threshold value, to permit the automatic engine stop due to the coast stop control at least once.