In this paper, we present a novel 2-D laser-based global localization approach for mobile robots, which is composed of geometrical relationship construction, a new structural unit encoding scheme (SUES), and an extended multiple hypothesis tracking (MHT) algorithm. Different from existing methods, we construct a 3-D “directional endpoint” feature encapsulating both the endpoint and the direction of a line segment; on this basis, a novel and efficient online structural unit encoding scheme (SUES) is proposed to describe the geometric relationship between the two directional endpoint features with some robustness to dynamic disturbances. Note that SUES presented in this paper is different from the bag-of-words scheme in two aspects: 1) SUES quantizes the geometrical relationship without offline training for vocabulary and 2) SUES is independent of the quality of the vocabulary. By factoring the global localization problem into a discrete pose estimation problem, the MHT is extended on the basis of SUES and odometry information to gradually restore the global robot pose. Different from the classical MHT framework, the extended MHT takes the independent observation results as the a priori , while the likelihood term is composed of consecutive candidate poses and the odometry information. Evaluations are carried out by using both publicly available data sets and self-recorded data sets. Comparative experimental results with respect to the adaptive Monte Carlo localization are presented to show the superior performance of the proposed approach in terms of success ratio and efficiency.