Only a single thorium fullerene, Th@C-84, has been reported to date (Akiyama, K.; et al. J. Nucl. Radiochem. Sci. 2002, 3, 151-154). Although the system was characterized by UV-vis and XANES (X-ray absorption near edge structure) spectra, its structure and properties remain unknown. In this work we used the density functional calculations to identify molecular and electronic structure of the Th@C-84. Series of molecular structures satisfying the ThC84 stoichiometric formula were studied comprising 24 IPR and 110 non-IPR Th@C-84 isomers as well as 9 ThC2@C-82 IPR isomers. The lowest energy structure is Th@C-84-C-s(10) with the singlet ground state. Its predicted electronic absorption spectra are in agreement with the experimentally observed ones. The bonding between the cage and Th was characterized as polar covalent with Th in formal oxidation state IV. The NMR chemical shifts of Th@C-84-C-s(10) were predicted to guide the future experimental efforts in identification of this compound.