In this paper, the vibrational spectra of copper sulfate hydrates (CuSO(4)·xH(2)O, x = 5, 3, 1, 0) have been investigated with low-temperature Raman spectroscopy and terahertz time domain spectroscopy (THz-TDS). It is found that the four groups of Raman bands between 90 and 4000 cm(-1) can be assigned to lattice vibration as well as intramolecular vibrations of a copper complex, sulfate group, and water molecules. The variation of vibrational spectra during the dehydrated process are discussed in detail considering the transformation of the crystal structure, especially the bands between 3000 and 3500 cm(-1), which are attributed to the ν(1) and ν(3) modes of water molecules. In addition, as a complement of Raman spectra, the THz spectra at 0.1-3 THz indicate the absorption due to the low-frequency lattice vibration and hydrogen bond.