Simultaneous localization and mapping (SLAM) are fundamental elements for many emerging technologies, such as autonomous driving and augmented reality. For this paper, to get more information, we developed an improved monocular visual SLAM system by using omnidirectional cameras. Our method extends the ORB-SLAM framework with the enhanced unified camera model as a projection function, which can be applied to catadioptric systems and wide-angle fisheye cameras with 195 degrees field-of-view. The proposed system can use the full area of the images even with strong distortion. For omnidirectional cameras, a map initialization method is proposed. We analytically derive the Jacobian matrices of the reprojection errors with respect to the camera pose and 3D position of points. The proposed SLAM has been extensively tested in real-world datasets. The results show positioning error is less than 0.1% in a small indoor environment and is less than 1.5% in a large environment. The results demonstrate that our method is real-time, and increases its accuracy and robustness over the normal systems based on the pinhole model.