Advances in 3D computer vision have increased the amount of point cloud data, highlighting the growing importance of point cloud sampling. Commonly used sampling methods like random sampling and farthest point sampling often fail to capture the geometric topology information of an object. We propose a skeleton-based point cloud sampling method to preserve the geometric topology information of the input point cloud. Skeletons have properties such as the extraction of global topology and the preservation of morphological features. Our method fully leverages these features to enhance the preservation of geometric topological information during the sampling stage. We utilize the variability of the local neighborhood normals as a prior information for sampling. Analyzing changes in skeleton normals facilitates the capture of salient points, enhancing the accuracy of point cloud sampling. To evaluate the effectiveness of our method, we conducted extensive comparative experiments using various sampling methods and scales, and found that it outperforms existing techniques.