Three-dimensional laser scanning is a new technology for fast acquisition of high-precision point clouds. However, due to the influence of the structure, roughness, texture of the object itself and measurement environment, the acquired point clouds mostly have isolated noise points. In view of the difficulty of removing complex noise in the point cloud data model of cultural relics, a denoising method for point cloud with geometric feature preservation is proposed. Firstly, the large-scale noise is deleted by rasterizing the point cloud, then the curvature factor and density factor of the data points in the point cloud are defined, and the clustering objective function of fuzzy C-means clustering (FCM) is constructed by weighting the factors. Finally, the small-scale noise is deleted by using the feature-weighted FCM algorithm, thus the denoising of point cloud is realized. The experimental results show that the denoising method for point cloud with geometric feature preservation has good denoising effect on cultural relics point cloud data, which is an effective point cloud denoising algorithm.