A driver-fatigue warning system suitable for use in an automated vehicle includes a camera, an alert-device, and a controller. The camera renders an image of a lane-marking and of an object proximate to a host-vehicle. The alert-device is operable to alert an operator of the host-vehicle of driver-fatigue. The controller is in communication with the camera and the alert-device. The controller determines a vehicle-offset of the host-vehicle relative to the lane-marking based on the image. The controller determines an offset-position of the object relative to the lane-marking based on the image. The controller determines that a lane-departure has occurred when the vehicle-offset is less than a deviation-threshold. The controller does not count occurrences of lane-departures when the offset-position is less than an offset-threshold, and activates the alert-device when the count of the occurrences of lane-departures exceeds a crossing-threshold indicative of driver-fatigue.