3D reconstruction is crucial for digitization of cultural relics, and the accuracy of 3D point cloud registration is a significant metric for evaluating the reconstruction quality. In practice, cultural relics point cloud data includes numerous details, and using conventional downsampling methods may result in the loss of such details, thereby affecting registration accuracy. We propose a point cloud classification downsampling and registering method for cultural relics based on curvature features. First, 3D point clouds data of cultural relics are obtained using linear matrix laser measurement. Next, the curvature values of all points are calculated, and a curvature threshold is set for point cloud classification. Different point sets are carried out downsampling with different weights according to their feature attributes to retain the shape features and details of the point cloud as much as possible. Finally, point cloud registration is achieved through calculating the rigid transformation model. Compared to the traditional global downsampling ICP method, the point cloud data of the downsampling processing before point cloud registration reduces to 1/3 of the original size. The average distance decreases from approximately 0.89 mm to 0.59 mm, while the standard deviation decreases from about 0.29 mm to 0.18 mm. This approach guarantees the accuracy of downsampling and registration and is applicable to various cultural relics point cloud data.