Recently, the interests in the 3D image, generated from the range data and CAD, have exceedingly increased, accordingly a various 3D image database is being constructed. The efficient and fast scheme to access the desired image data is the important issue in the application area of the Internet and digital library. However, it is difficult to manage the 3D image database because of its huge size. Therefore, a proper descriptor is necessary to manage the data efficiently, including the content-based search. In this paper, the proposed shape descriptor is based on the voxelization of the 3D image. The medial axis transform, stemming from the mathematical morphology, is performed on the voxelized 3D image and the graph, which is composed of nodes and edges, is generated from skeletons. The generated graph is adequate to the novel shape descriptor due to no loss of geometric information and the similarity of the insight of the human. Therefore the proposed shape descriptor would be useful for the recognition of 3D object, compression, and content-based search.