An engine control device in a vehicle in which an output of an engine is transmitted to a driving wheel through a transmission, and a lockup mechanism is disposed between the engine and the transmission, and is configured to allow relative rotation between the engine and the transmission, the engine control device comprising: a sensor for sensing an operating state of the vehicle; and a controller connected to the sensor, wherein the controller is configured to: stop fuel injection of the engine, when engine rotational speed (Ne) is above a preset specific fuel cut-off rotational speed while the vehicle is coasting; restart the fuel injection, when the engine rotational speed (Ne) 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; determine whether or not the operating state allows the stop and restart of fuel injection to be repeated; and setting a hunting-preventing fuel cut-off rotational speed higher than the specific fuel cut-off rotational speed, and lower than or equal to an input shaft rotational speed of the transmission, when determining that the operating state allows the stop and restart of fuel injection to be repeated, wherein the hunting-preventing fuel cut-off rotational speed replaces the specific fuel cut-off rotational speed. a sensor for sensing an operating state of the vehicle; and a controller connected to the sensor, wherein the controller is configured to: stop fuel injection of the engine, when engine rotational speed (Ne) is above a preset specific fuel cut-off rotational speed while the vehicle is coasting; restart the fuel injection, when the engine rotational speed (Ne) 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; determine whether or not the operating state allows the stop and restart of fuel injection to be repeated; and setting a hunting-preventing fuel cut-off rotational speed higher than the specific fuel cut-off rotational speed, and lower than or equal to an input shaft rotational speed of the transmission, when determining that the operating state allows the stop and restart of fuel injection to be repeated, wherein the hunting-preventing fuel cut-off rotational speed replaces the specific fuel cut-off rotational speed. stop fuel injection of the engine, when engine rotational speed (Ne) is above a preset specific fuel cut-off rotational speed while the vehicle is coasting; restart the fuel injection, when the engine rotational speed (Ne) 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; determine whether or not the operating state allows the stop and restart of fuel injection to be repeated; and setting a hunting-preventing fuel cut-off rotational speed higher than the specific fuel cut-off rotational speed, and lower than or equal to an input shaft rotational speed of the transmission, when determining that the operating state allows the stop and restart of fuel injection to be repeated, wherein the hunting-preventing fuel cut-off rotational speed replaces the specific fuel cut-off rotational speed.