1. A white road line recognition device for a vehicle comprising: white road line border point detecting means that detects a pair of white road line edge points that includes a white road line starting point and a white road line ending point on a plurality of retrieval lines set in the horizontal direction in a captured image of a driving environment of an own vehicle, based on a change in luminance on the retrieval lines; midpoint calculating means that calculates a midpoint between the white road line starting point and the white road line ending point detected on the retrieval lines; point group selecting means that selects a point group, as the point group having the smallest dispersion, from among: at least either of a point group consisting of the white road line starting points, or a point group consisting of the white road line ending points; and a point group consisting of the midpoints, according to a predetermined condition; and white road line calculating means that calculates a white road line based on the selected point group, wherein the point group selecting means obtains an approximation formula which expresses the point groups using a Hough transform, compares a peak value of frequency on the Hough plane obtained by the calculation among the point groups, and selects a point group that has the largest peak as the point group with a smallest dispersion.