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 starting point and a white road line ending point for each of retrieval lines set in the horizontal direction in a captured image of driving environment of an own vehicle, based on the change in luminance on the retrieval lines; midpoint calculating means that calculates a midpoint of the white road line starting point and the white road line ending point detected on each of the retrieval lines; point group selecting means that selects a point group with a smallest dispersion among at least either of a point group consisting of the white road line starting points or a point could 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.