For the SLAM system in robotics and autonomous driving, the accuracy of front-end odometry and back-end loop-closure detection determine the whole intelligent system performance. But the LiDAR-SLAM could be disturbed by current scene moving objects, resulting in drift errors and even loop-closure failure. Thus, the ability to detect and segment moving objects is essential for high-precision positioning and building a consistent map. In this paper, we address the problem of moving object segmentation from 3D LiDAR scans to improve the odometry and loop-closure accuracy of SLAM. We propose a novel 3D Sequential Moving-Object-Segmentation (3D-SeqMOS) method that can accurately segment the scene into moving and static objects, such as moving and static cars. Different from the existing projected-image method, we process the raw 3D point cloud and build a 3D convolution neural network for MOS task. In addition, to make full use of the spatio-temporal information of point cloud, we propose a point cloud residual mechanism using the spatial features of current scan and the temporal features of previous residual scans. Besides, we build a complete SLAM framework to verify the effectiveness and accuracy of 3D-SeqMOS. Experiments on SemanticKITTI dataset show that our proposed 3D-SeqMOS method can effectively detect moving objects and improve the accuracy of LiDAR odometry and loop-closure detection. The test results show our 3D-SeqMOS outperforms the state-of-the-art method by 12.4%. We extend the proposed method to the SemanticKITTI: Moving Object Segmentation competition and achieve the 2nd in the leaderboard, showing its effectiveness.