1. A vehicle periphery monitoring device comprising: a plurality of imaging units mounted on a vehicle and configured to capture images of a vehicle periphery; an image brightness calculation processor configured to calculate a value corresponding to brightness of images taken by the plurality of imaging units; a brightness correction unit, said brightness correction unit being configured to correct the brightness of the images obtained by the plurality of imaging units on the basis of the value calculated by the image brightness calculation processor; an image combining processor configured to combine the plurality of images obtained by the plurality of imaging units and corrected by the brightness correction unit into a single image; an image convertor that converts the single image formed by the image combining processor into an overhead image viewed from right above the vehicle; a traveling direction judgment processor configured to judge a traveling direction of a vehicle; an imaging-unit-selecting processor configured to select one image from the images taken by the plurality of imaging units on the basis of a judgment result of the traveling direction judgment processor; and an image display unit that simultaneously displays the overhead image formed by the image convertor and one image selected by the imaging-unit-selecting processor; wherein the image brightness calculation processor calculates a value corresponding to brightness of the image imaged by the imaging unit corresponding to a traveling direction of the vehicle based on the determination result of the traveling direction judgment processor and selected by the imaging-unit-selecting processor, the brightness correction unit corrects brightness of the images taken by the plurality of imaging units other than the imaging unit corresponding to the traveling direction based on the difference between the value corresponding to the brightness of the image taken by the imaging unit in the traveling direction and calculated by the image brightness calculation processor and the values corresponding to brightness of the others of the plurality of the imaging units for an image area which is overlapped on the image area of the traveling direction, and the image display unit simultaneously displays the overhead image combined by the image combining processor and converted by the image convertor and the image selected by the imaging-unit-selecting processor, the brightness of the combined and converted overhead image being corrected.