Despite its experimental characterization, the detailed geometry and electronic structure of actinide metallofullerene U@C-82 have been rarely studied. We predict that C-#5(82) and C-#8(82) are the best cages for the encapsulation of monovalent and tetravalent U (i.e., U+ and U4+), respectively; while C-#9(82) is the best cage for divalent, trivalent, pentavalent, and hexavalent U cations (i.e., U2+, U3+, U5+, and U6+). U@C-#9(82) is the thermodynamically most stable one among all the isomers and thus corresponds to the most experimentally isolable isomer of U@C-82. The calculated spin density explicitly suggests that the endohedral metallofullerene U@C-#9(82) is a trivalent ion-pair with an electronic configuration of U3+@C-82(3-). The proposed geometry and electronic structure of U3+@C-#9(82)3- are in good agreement with the experimental observation.