In this paper, we propose a vision-based simultaneous localization and map-building (SLAM) algorithm using compressed extended Kalman filter (CEKF). SLAM addresses the problem of locating a mobile robot in unknown environments. Extended Kalman filters (EKF) are widely used to solve this problem. However, this filter is very time consuming. To reduce the computational complexity, we apply a CEKF to stereo images while compensating for some of the limitation shown in previous implementations of CEKF. Moreover, we estimate the full DOF, its position and pose, of the mobile robots which is required when operating in the outdoor environment. Outdoor experiments have been conducted to test the effectiveness of the proposed SLAM algorithm.