1. A travel division line recognition apparatus mounted to an own vehicle, comprising: an extracting unit that extracts a travel division line candidate from an image of a surrounding environment including a road, captured by an on-board camera mounted in the own vehicle, the travel division line candidate being a candidate for a travel division line on the road; a calculating unit that calculates a degree of reliability that the travel division line candidate extracted by the extracting unit will be the travel division line; and a recognizing unit that selects the travel division line candidate based on the degree of reliability calculated by the calculating unit, and recognizes the travel division line using the selected travel division line candidate, the calculating unit including: a solid object processing unit that recognizes solid objects including vehicles, sets a suppression area based on the recognized solid objects, and reduces the degree of reliability of the travel division line candidate present within the suppression area, the suppression area including: a frontal-face suppression area that is set so as to cover a frontal face of another vehicle in a position in which the frontal face has been recognized; and a side-face suppression area that is set so as to cover a side face that is formed by extending the frontal-face suppression area in a depth direction by a predetermined vehicle length.