Point cloud registration plays a crucial role in mobile robot localization, map building and 3D model reconstruction. However, it remains challenged by issues such as compromised accuracy and sluggish efficiency, posing significant obstacles in achieving precise and timely alignments. Therefore, we propose a lightweight and fast point cloud registration method. Firstly, we mesh the 3D point cloud, compared with the traditional gridded point cloud method, it achieves initial point cloud registration by preserving the curvature characteristics of the internal point cloud, and utilizing the spatial relationship between grid cells and the quantitative relationship between the internal point cloud. Moreover, we adopt an iterative nearest point (ICP) based on KD-Tree to realize the fine registration. So, our method does not necessitate intricate feature analysis and data training, and is resilient to similar transformations, non-uniform densities and noise. Finally, we conduct point cloud registration experiments using multiple publicly available point cloud datasets and compare them with several point cloud registration methods. The results demonstrate it is able to accomplish the point cloud registration quickly and exhibit high accuracy. More importantly, it maintains its efficacy and robustness even in the presence of noisy and defective point clouds.