We report here the measurements of the valence spectra, the C 1s and the Si 2p core-level spectra of C60 molecules adsorbed on a Si(111)-(7X7) surface, using photoelectron spectroscopy. In the valence spectra, the highest occupied molecular orbital (HOMO) of a C60 splits into two peaks at a coverage lower than 0.25 ML. The binding energies of the split peaks are 1.8 and 2.4 eV. Taking into account the polarization-dependence of the valence spectra and the binding energy of the C 1s core-level spectra, it is found that the 2.4-eV peak observed in the valence spectra is the covalent bonding state between a C60 molecule and the Si substrate, and that the 1.8-eV peak is the shifted HOMO. The Si 2p core-level spectra suggest that the bonding site is localized at the interface. We also present the energy-level scheme of the bonding state in terms of the symmetry of the HOMO.