In a Global Navigation Satellite System (GNSS)-restricted area, a mobile robot navigation system exploits surrounding environment information. For an aerial or underwater vehicle, undulating terrain of a land or seabed surface is a valuable information resource that leads to the development of terrain-referenced navigation (TRN) algorithms. However, due to the vast amount of a vehicle's activity area, surveying all the regions to obtain a high-resolution terrain map is impractical and requires simultaneous localization and mapping (SLAM) as a highly desirable capability. This paper presents a topographic SLAM algorithm using only a single terrain altimeter, which is low-cost, computationally efficient, and sufficiently stable for long-term operation. The proposed rectangular panel map structure and update method enable robust and efficient SLAM. As terrain elevation changes are inherently nonlinear, an extended Kalman filter (EKF)-based SLAM filter is adopted. The feasibility and validity of the proposed algorithm are demonstrated through simulations using terrain elevation data from a real-world undersea environment.