This paper suggests a new observation model for Extended Kalman Filter based Simultaneous Localization and Mapping (EKF-SLAM). Since the EKF framework linearizes non-linear functions around the current estimate, the conventional line model has large linearization errors when a mobile robot locates faraway from its initial position. On the other hand, the model that we propose yields less linearization error with respect to the landmark position and thus suitable in a large-scale environment. To achieve it, we build up a three-dimensional space by adding a virtual axis to the robot’s two-dimensional coordinate system and extract a plane by using a detected line on the two-dimensional space and the virtual axis. Since Jacobian matrix with respect to the landmark position has small value, we can estimate the position of landmarks better than the conventional line model. The simulation results verify that the new model yields less linearization errors than the conventional line model.