The electronic structure, vibrational and dielectric properties of MoS2 were studied by first-principles based on density functional theory (DFT). The band structure, density of states, the dielectric function spectrum and the infrared reflectivity spectrum were presented. The results indicate that MoS2 is a semiconductor with indirect band gap. The dielectric tensors are highly anisotropic. It is found that lattice vibration makes less contribution to the dielectric constant than that of electronic screening. Due to the existence of Infrared active modes over the range of 300~500 cm-1, there is a strong interaction between the material and electromagnetic wave, impairing the wave-transparent properties of MoS2.