In this paper we propose a fast 3D pose based SLAM system that estimates a vehicle’s trajectory by registering sets of planar surface segments, extracted from 360∘360∘ field of view (FOV) point clouds provided by a 3D LIDAR. Full FOV and planar representation of the map gives the proposed SLAM system the capability to map large-scale environments while maintaining fast execution time. For efficient point cloud processing we apply image-based techniques to project it to three two-dimensional images. The SLAM backend is based on Exactly Sparse Delayed State Filter as a non-iterative way of updating the pose graph and exploiting sparsity of the SLAM information matrix. Finally, our SLAM system enables reconstruction of the global map by merging the local planar surface segments in a highly efficient way. The proposed point cloud segmentation and registration method was tested and compared with the several state-of-the-art methods on two publicly available datasets. Complete SLAM system was also tested in one indoor and one outdoor experiment. The indoor experiment was conducted using a research mobile robot Husky A200 to map our university building and the outdoor experiment was performed on the publicly available dataset provided by the Ford Motor Company, in which a car equipped with a 3D LIDAR was driven in the downtown Dearborn Michigan.