This paper presents a new approach based on scan matching for global localization with a metric-topological hybrid world model. The proposed method aims to estimate relative pose to the most likely reference site by matching an input scan with reference scans, in which topological nodes are used as reference sites for pose hypotheses. In order to perform scan matching we apply the spectral scan matching (SSM) method that utilizes pairwise geometric relationships (PGR) formed by fully interconnected scan points. The SSM method allows the robot to achieve scan matching without using an initial alignment between two scans and geometric features such as corners, curves, or lines. The localization process is composed of two stages: coarse localization and fine localization. Coarse localization with 2D geometric histogram constructed from the PGR is fast, but not precise sufficiently. On the other hand, fine localization using the SSM method is comparatively slow, but more accurate. This coarse-to-fine framework reduces the computational cost, and makes the localization process reliable. The feasibility of the proposed methods is demonstrated by results of simulations and experiments.