In an apparatus for determining a traveling position of an own vehicle that is an autonomous driving vehicle equipped with the apparatus, a judgment section is configured to judge presence or absence of at least one of a travel history of other vehicles regarding the lane in which the own vehicle is traveling and an object that is located in the vicinity of the own vehicle within the lane in which the own vehicle is traveling and should be avoided coming into contact with. The traveling position is a widthwise position of the own vehicle within a lane in which the own vehicle is traveling. A determination section is configured to determine the traveling position using the travel history in response to the judgment section judging that the travel history exists and using position information of the object in response to the judgment section judging that the object exists.