We apply a Su-Schriefter-Heeger-like model to study intramolecular electron-phonon interaction for the undoped C60 molecule in which all the translational degrees of freedom for each site are considered. We find that the C60 molecule favors a dimerized ground state and the inclusion of the electron-phonon coupling modifies the phonon spectra such that all the frequencies of the phonon modes shift to red except the A"mode. We also present a semianalytical treatment for the ground-state properties supplemented to the numerical calculations.