In current visual SLAM methods, point-like landmarks (As in Filliat and Meyer (Cogn Syst Res 4(4):243-282, 2003), we use this expression to denote a landmark generated by a point or an object considered as punctual.) are used for representation on maps. As the observation of each point-like landmark gives only angular information about a bearing camera, a covariance matrix between point-like landmarks must be estimated in order to converge with a global scale estimation. However, as the computational complexity of covariance matrices scales in a quadratic way with the number of landmarks, the maximum number of landmarks that is possible to use is normally limited to a few hundred. In this paper, a visual SLAM system based on the use of what are called rigid-body 3D landmarks is proposed. A rigid-body 3D landmark represents the 6D pose of a rigid body in space (position and orientation), and its observation gives full-pose information about a bearing camera. Each rigid-body 3D landmark is created from a set of N point-like landmarks by collapsing 3N state components into seven state components plus a set of parameters that describe the shape of the landmark. Rigid-body 3D landmarks are represented and estimated using so-called point-quaternions, which are introduced here. By using rigid-body 3D landmarks, the computational time of an EKF-SLAM system can be reduced up to 5.5%, as the number of landmarks increases. The proposed visual SLAM system is validated in simulated and real video sequences (outdoor). The proposed methodology can be extended to any SLAM system based on the use of point-like landmarks, including those generated by laser measurement.