As a significant geometric feature of 3D point clouds, sharp features play an important role in shape analysis, 3D reconstruction, registration, localization, etc. Current sharp feature detection methods are still sensitive to the quality of the input point cloud, and the detection performance is affected by random noisy points and non-uniform densities. In this paper, using the prior knowledge of geometric features, we propose a Multi-scale Laplace Network (MSL-Net), a new deep-learning-based method based on an intrinsic neighbor shape descriptor, to detect sharp features from 3D point clouds. Firstly, we establish a discrete intrinsic neighborhood of the point cloud based on the Laplacian graph, which reduces the error of local implicit surface estimation. Then, we design a new intrinsic shape descriptor based on the intrinsic neighborhood, combined with enhanced normal extraction and cosine-based field estimation function. Finally, we present the backbone of MSL-Net based on the intrinsic shape descriptor. Benefiting from the intrinsic neighborhood and shape descriptor, our MSL-Net has simple architecture and is capable of establishing accurate feature prediction that satisfies the manifold distribution while avoiding complex intrinsic metric calculations. Extensive experimental results demonstrate that with the multi-scale structure, MSL-Net has a strong analytical ability for local perturbations of point clouds. Compared with state-of-the-art methods, our MSL-Net is more robust and accurate. The code is publicly available at.