Ab initio molecular orbital theory was used to examine the hydrogenation of a C-60 molecule. The 1,2 addition of the 6,6 bond is an energetically favorable adsorption site in one-hydrogen-molecule adsorption. We found that the averaged C-H bond energy is maximized in the C60H36 Molecule. Calculation of the Gibbs free energy of the C-60 + 30 H-2 --> C60H60 reaction showed that this reaction becomes endothermic above 220 K. Moreover, the C-H bond energy associated with the increasing number of six-membered rings found to decrease by calculating the averaged C-H bond energies of five fully hydrogenated fullerenes: C20H20, C36H36, C60H60, C70H70, and C90H90.