Laser SLAM is a key enabling technology for autonomous navigation of intelligent mobile robots. The standard FLOAM algorithm experiences low positioning accuracy, weak anti-interference performance, and prone error accumulation in pure LiDAR scenarios, making it difficult to meet practical engineering requirements. The focus of numerous studies is thus on improved pure laser SLAM algorithms that are highly robust. The enhanced algorithm of FLOAM GICP registration and SOR filtering is applied in this study. The SOR filtering processes the laser point cloud to remove outlier noise. The GICP registration replaces the classic with an optimized matching cost function. Experiments are conducted on a mobile robot with a Leishen C16 LiDAR to simulate real-life tests in an indoor corridor and outdoor plaza on the Gazebo simulation platform. The results from the EVO tool’s quantitative evaluation indicate that the indoor mean absolute error and RMSE were reduced by 46.67% and 41.67% compared with FLOAM. The outdoor mean and maximum errors are reduced by 46.00% and 70.00%, respectively. The proposed improved scheme achieves centimeter-level positioning accuracy and strong robustness in pure laser configurations without auxiliary sensors such as IMUs or odometers, providing a reliable technical solution for the engineering application of mobile robots in sensor-constrained scenarios.