1. A cruise control system for a vehicle, comprising: a position change detector which detects, from information on a road existing in a frontward direction of the vehicle, a horizontal distance from a line segment orthogonal to a traveling direction vector of the vehicle, to a centerline of the road, the detection being conducted at a plurality of measuring points in an extending direction of the traveling direction vector; a road shape recognizer which identifies a shape of the road from data relating to linearity of changes in each of the horizontal distances, the linearity data being obtained by said position change detector; and a cruise controller which controls traveling of the vehicle according to results of the identification by said road shape recognizer.