This paper presents a novel framework for 3D object content-based search and retrieval, appropriate for both partial and global matching applications. The framework is based on a graph representation of a 3D object which is enhanced by local geometric features. The 3D object is decomposed into meaningful parts and an attributed graph is constructed based on the connectivity of the parts. Every 3D part is approximated with a suitable superellipsoid and a novel 3D shape descriptor, called 3D Distance Field Descriptor, is computed and associated to the corresponding graph nodes. The matching process used is based on attributed graph matching algorithm appropriate for this application. The proposed method not only provides successful retrieval results in terms of geometric similarity but also is invariant to rotation, translation and scaling of an object as well as to the different poses of articulated objects. Finally, it can be effectively used for partial and global 3D object retrieval.