Simultaneous localization and mapping (SLAM) is considered as the core of building high-precision three-dimensional environmental maps. For this, we proposed a high-precision laser-based SLAM system. Aiming at the problem that the point cloud data obtained from laser is not representative and the iterative closest point method for calculating pose transformation is time-consuming, we proposed an efficient and stable matching algorithm. It uses fused feature points to align with the occupancy grid submaps with less registration error and is less time-consuming. Then, to address the problem in which the registration result falls into the local optimum early, we proposed a quadratic registration algorithm. This method effectively improves the initial value of the registration process. Finally, a time consistency and global consistency loop detection algorithm are used to reduce the cumulative error. The system we proposed has been tested on the University of Michigan North Campus Long-Term dataset and Cartographer dataset. Experiments show that our system has good accuracy under low-speed motion conditions (speeds ranging from 1 to 2  m  /  s).