Ab initio effective core potential calculations have been carried out on Hf8C12 metallo-carbohedrene cluster. First, the geometries of the ground states have been optimized for structures of T and Td-symmetry, respectively. It has been shown that the Td-symmetry structure is more stable than T's. Then Hf8C12 cluster with Td-symmetry is studied by unlimited Hartree-Fock method and Natural Bonding Orbital analyzing. It has been found that there are three stable states of different spins, which are related to the bonding mechanism, electronic configuration and structure of the electron energies. For S=0, the Hf。atoms of the outer tetrahedron link the six ethylene-like C2units through Hf—C polar covalent bonds within Hf8C12 cluster. For S=1, six acetylene-like C2 units are adsorpted on the Hf8 framework. For S=2, some ｐπ bonds on the C2 units are found broken and bonded with Hf atoms in d←ｐπ bond-type. Most of Hf—C bonds are of Hf。—C type. Furthermore, it is found that the structure model of Hf8C12 cluster with Td-symmetry is (Hf8)+4.5(C-0.752)6, which is ferromagnetic at the high spin states. Meanwhile, the distribution of electron energies also changes with spin states.