Purpose: Localization and mapping with LiDAR data is a fundamental building block for autonomous vehicles. Though LiDAR point clouds can often encode the scene depth more accurate and steadier compared with visual information, laser-based Simultaneous Localization And Mapping (SLAM) remains challengeable as the data is usually sparse, density variable and less discriminative. The purpose of this paper is to propose an accurate and reliable laser-based SLAM solution. Design/methodology/approach: The method starts with constructing voxel grids based on the 3D input point cloud. These voxels are then classified into three types to indicate different physical objects according to the spatial distribution of the points contained in each voxel. A global environment model with Partition of Unity (POU) implicit surface is maintained along the process and located voxels are merged into it from stage to stage, through scan-to-model matching implemented by Levenberg-Marquardt method. Findings: We find a laser-based SLAM method. The method uses POU implicit surface representation to build the model and is evaluated on the KITTI odometry benchmark without loop closure. Experimental results indicate that the method achieves accuracy comparable to the state-of-the-art methods. Originality/value: We propose a novel, low-drift SLAM method, which falls into a scan-to-model matching paradigm, operates on point clouds obtained from Velodyne HDL64. The method is of value to researchers developing SLAM systems for autonomous vehicles.