The rotational and vibrational dynamics of molecules in copper sulfate pentahydrate crystal are investigated with terahertz dielectric spectra. It is shown that the relaxation-like dielectric dispersion in the low frequency region is related to the reorientation of water molecules under the driving of terahertz electric field, whereas the resonant dispersion can be ascribed to lattice vibration. It is also found that, due to the hydrogen-bond effect, the vibrational mode at about 1.83 THz along [-111] direction softens with decreasing temperature, that is, the crystal expands in this direction when cooled. On the contrary, the mode hardens in the direction perpendicular to [-111] during the cooling process. This contributes to the further understanding of the molecular structure and bonding features of hydrate crystals.