Vibrational frequencies of guest molecules in clathrate hydrates reflect the molecular environment and dynamical behavior of molecules. A detailed understanding of the mechanism for the vibrational frequency changes of the guest molecules in the clathrate hydrate cages is still incomplete. In this study, molecular vibrations of methane molecules in a structure I clathrate hydrate are calculated from ab initio molecular dynamics simulation. The vibrational spectra of methane are computed by Fourier transform of autocorrelation functions, which reveal distinct separation of each vibrational mode. Calculated symmetric and asymmetric stretching vibrational frequencies of methane molecules are lower in the large cages than in the small cages (8 and 16 cm(-1) for symmetric and asymmetric stretching, respectively). These changes are closely linked with the C-H bond length. The vibrational frequencies for the bending and rocking vibrational modes nearly overlap in each of the cages.