It is very important for a mobile robot to estimate its current position. With precise information about the current position, the mobile robot can plan a path and execute its missions. Among many methods for self-localization, a vision-based approach is simple and flexible. In this thesis, a position estimation method using 1-D perspective invariant(Cross Ratio) is presented. Since this method uses a simple cross ratio, building and updating of map and database matching process become trivial tasks. The algorithm is based on two basic assumptions that the ground is flat and two locally parallel side lines are available. Intersection points between two locally parallel side lines and the vertical lines of doors, which are the given landmarks, are used as point features to compute cross ratio. As an off-line process, the database for matching, which consists of the cross ratios of the point features in the map database, is constructed. A mobile robot takes an image of corridors and computes the cross ratios for a set of point features in the image and a vanishing point which is the intersection point of two parallel side lines. Then, it searches for the matching point features using geometric hashing. Using the vanishing point and the corresponding point features, the mobile robot calculates its current orientation and position. We demonstrate the robustness and feasibilities of our algorithm through real world experiments in indoor environment.