Reconstruction of three-dimensional (3D) models from images is currently one of the most important areas of research in computer vision. In this paper, we propose a method to recover 3D models using the minimum number of line segments. By using structure-from-motion, the proposed method first recovers a 3D model of line segments detected from an input image sequence. We then detect overlapping 3D line segments that redundantly represent a single line structure so that the number of 3D line segments representing the target scene can be reduced without losing the detailed geometry of the structure. We apply matching and depth information to remove redundant line segments from the model while keeping the necessary segments. In experiments, we confirm that the proposed method can greatly reduce the number of line segments. We also demonstrate that the accuracy and computational time for camera pose estimation can be significantly improved with the 3D line segment model recovered by the proposed method. Moreover, we have applied the proposed method to see through occluded areas.