The generalized gradient approximation based on the density functional theory is used to analyze the geometric and the electronic properties of C80H80. The geometric structure research indicates that between the two possible stable isomers, the isomer with 20 hydrogens connecting 12 pentagons and the 60 others outside is more stable structure. The analyses of the energy level, the orbital wavefunction, and the density of states of H20@C80H60, show that the atomic orbits of the H and C atoms have strong hybridization on the occupied molecular orbits. The low unoccupied molecular orbital of H20@C80H60 is occupied mainly by the H atoms inside the carbon cage, while the high occupied molecular orbital of H20@C80H60 are occupied partly by the H atoms outside the cage. Therefore, the H atoms inside and outside the cage will play different roles in the chemical reaction involving H20@C80H60. The H20@C80H60 shows the character of the closed-shell structures with no magnetic moment.