This paper proposes an algorithm capable of extracting corresponding points between a pair of stereo images based on dynamic programming. The purpose of extracting the corresponding points is to provide the stereo disparity data to a road-slope estimation algorithm with high accuracy and in real-time. As the road-slope estimation algorithm does not require dense disparity data, the proposed stereo matching algorithm aims at extracting corresponding points accurately and quickly. In order to realize this contradictory goal, this paper exploits dynamic programming, and minimizes matching candidates using vertical components of color edges. Furthermore, the typical occlusion problem in stereo vision is solved. The proposed algorithm is proven to be effective through experiments with various images captured on the roads.