This study proposes a fast and accurate new edge-extraction method based on the Gaussian map clustering algorithm. First, the normals in the Gaussian sphere are clustered via agglomerative clustering and normal estimation. Then, the covariance matrix eigenvalues of the nearest neighbors of each point are analyzed to detect the edge features. The edge-extraction experiments are performed on different pointcloud objects, and the edge extraction effects and the extraction time are compared and analyzed. The experimental results indicate that the proposed method can quickly and efficiently extract the edge features from point clouds and its performance is improved compared with the edge-extraction algorithm based on original Gaussian map clustering.