This paper describes an efficient localization algorithm based on a vector-matching technique for mobile robots with laser range finders. As a reference the method uses a map with line-segment vectors, which can be built from a CAD layout of the indoor environment. The contribution of this work lies in the overall localization process. First, the proposed sequential segmentation method enables efficient vector extraction from scanned data. Second, a reliable and efficient vector-matching technique is proposed. Finally, a cost function suitable for vector-matching is proposed for nonlinear pose estimation with solutions for both nonsingular and singular cases. Simulation results show that the proposed localization method works reliably even in a noisy environment. The algorithm was implemented for our wheelchair-based mobile robot and evaluated in a 135 m long corridor environment.