Simultaneous Localization and Mapping (SLAM) is the process of building a map of an unknown environment and simultaneously localizing a robot relative to this map. SLAM is very important for the indoor navigation of a mobile robot and much research has been conducted on this subject. Although feature-based SLAM using an Extended Kalman Filter (EKF) is widely used, it has shortcomings in that the computational complexity grows in proportion to the square of the number of features. This prohibits EKF-SLAM from operating in real time and makes it unfeasible in large environments where many features exist. This paper presents an algorithm which reduces the computational complexity of EKF-SLAM by using topological information (TI) extracted through a thinning process. The global map can be divided into local areas using the nodes of a thinning-based topological map. SLAM is then performed in local instead of global areas. Experimental results for various environments show that the performance and efficiency of the proposed EKF-SLAM/TI scheme are excellent.