No / Both prominent feature points and geodesic distance are key factors for mesh segmentation. With these two factors, this paper proposes a graph cut based mesh segmentation method. The mesh is first preprocessed by Laplacian smoothing. According to the Gaussian curvature, candidate feature points are then selected by a predefined threshold. With DBSCAN (Density-Based Spatial Clustering of Application with Noise), the selected candidate points are separated into some clusters, and the points with the maximum curvature in every cluster are regarded as the final feature points. We label these feature points, and regard the faces in the mesh as nodes for graph cut. Our energy function is constructed by utilizing the ratio between the geodesic distance and the Euclidean distance of vertex pairs of the mesh. The final segmentation result is obtained by minimizing the energy function using graph cut. The proposed algorithm is pose-invariant and can robustly segment the mesh into different parts in line with the selected feature points.