This apparatus specifies, based upon the front image that is photographed by a front camera 65f before the present time by a predetermined time, the position (point A) of the "object" in the front image by utilizing the difference in brightness, and specifies, based upon the rear image photographed by a rear camera 65r at the present time, the position (point C) of the object same as the aforesaid "object" in the rear image by utilizing the difference in brightness. This apparatus obtains the displacement amount m in the image lateral direction of the position (point C) of the specified "same object" in the rear image with respect to the position (point B) of the aforesaid "same object" in the rear image that is to be specified supposing that the vehicle body slip angle .theta. is "0", and detects the vehicle body slip angle .theta. according to the equation of ".theta.=tan.sup.-1(m/L)" (L: camera-to-camera distance).