In a vehicle in which an output of an engine is transmitted to a driving wheel through a transmission, an engine control device stops fuel injection of the engine, when engine rotational speed is above a preset specific fuel cut-off rotational speed while the vehicle is coasting; and restarts the fuel injection, when the engine rotational speed falls below a recovery rotational speed while the fuel injection is stopped, wherein the recovery rotational speed is below the specific fuel cut-off rotational speed. When determining that an operating state allows the stop and restart of fuel injection to be repeated, the engine control device sets a hunting-preventing fuel cut-off rotational speed based on an input shaft rotational speed of the transmission, wherein the hunting-preventing fuel cut-off rotational speed replaces the specific fuel cut-off rotational speed.