A control apparatus of a work vehicle includes a course data acquisition unit acquiring course data indicating a traveling condition of a work vehicle that includes a travel route, a travel range data acquisition unit acquiring travel range data indicating a travel range of the work vehicle that is defined with a preset travel width based on the travel route, a detection data acquisition unit acquiring detection data of a detection device that has detected a travel direction of the work vehicle, a prediction unit predicting, based on the detection data, a prescribed position distant from a current position of the work vehicle traveling according to the course data, a determination unit determining whether the prescribed position exists within the travel range, and a drive control unit stopping traveling of the work vehicle when it is determined that the prescribed position does not exist within the travel range.