Terahertz time-domain spectroscopy (THz-TDS) is used to study the spectral response of lithium niobate crystals (LiNbO3) in the far infrared region. The optical constants are derived from the measured complex refractive index.A giant birefringence is observed in this material, and the average refractive-index difference between the ordinary wave and the extraordinary wave, no - ne, can reach up to about 1.6. Such a large birefringence is attributed to the different phonon modes of A1 (z) and E(x, y). This unusual property makes LiNbO3 a promising material to be used as a functional material in the terahertz region, e.g. Employed as wave-plates and polarization separators.