Different composition Hg1-xCdxTe crystals were grown by THM method. The optical properties of Hg1-xCdxTe crystals were investigated by using the Fourier transform infrared spectroscopy and transmission mode THz time-domain spectroscopy. The transmission was approached to zero in 0.2~1.5 THz frequency range as Cd composition of Hg1-xCdxTe crystal was lower than 0.279. A TA phonon model of Hg1-xCdxTe crystal was observed at 0.9 THz. Drude model was applied for simulation, which fitted well with the experimental results. The carrier densities of the Hg1-xCdxTe (x=0.388 and 0.326) were also characterized, which agreed with the experimental results.