Edges in a point cloud are important intermediate features for structuring point clouds and converting them into high-quality surfaces or solid models. To effectively extract the edge of the point cloud, an adaptive point cloud edge detection method based on local edge feature descriptor is proposed herein. The proposed method aims at addressing the problem of inaccurate edge detection caused by setting a unified neighborhood value or neighborhood radius in the existing point cloud edge detection algorithm. First, we provide the definition of a normal vector feature model, introduce the normal vector change rate, and propose a neighborhood adaptive method based on the normal vector change rate. Second, we combine the curvature density of the local area of the point cloud to define the local edge feature descriptor. Finally, we automatically adjust the threshold according to the characteristics of the value of the feature descriptor consistent with the Gaussian distribution, which solves the problem of manually adjusting the parameters for different point cloud models. Experiments on a variety of different point cloud datasets prove that the algorithm can accurately extract model edge information while maintaining the original information of the model. Furthermore, it exhibits repeatability and certain degree of robustness.