In urban dynamic environment, most of the existing works on LiDAR SLAM are based on static scene assumption and are greatly affected by dynamic obstacles. In order to solve this problem, this paper is based on F-LOAM, and adopts FA-RANSAC algorithm, improved ScanContext algorithm and global optimization to propose a robust and fast LiDAR Odometry and Mapping (RF-LOAM). Firstly, the Region Growing algorithm is used to cluster the fan-shaped grids. Then, we propose FA-RANSAC algorithm base on feature information and adaptive threshold for dynamic objects removal, and extracts the static edge and planar feature points for the first distortion compensation. Afterward, estimated pose is calculated by the static feature points and is used to perform the second distortion compensation. Then, the height difference and adaptive distance threshold are used to improve the accuracy of ScanContext, and the efficiency of ScanContext is improved by deleting the loop closure historical matching frames and simplifying the feature matching. Finally, global optimization is used for keyframe. The experimental tests are carried out on the KITTI datasets, Urbanloco datasets and our Extracted dataset. The results show that compared with the state-of-the-art SLAM methods, our method can not only accurately complete dynamic objects removal and loop closure detection, but also achieve more robust and faster localization and mapping in urban dynamic scenes.