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In order to further understand the electronic structure and the optical properties of MoS2, using the first-principle and based on density functional theory, the electronic structure and the optical properties of single-layer MoS2 were calculated and analyzed by the plane wave pseudo-potential method. Band structure, density of states, and optical absorption, reflection, energy loss, optics constants and dielectric function spectra of monolayer MoS2 were obtained. The calculation results show that the single-layer MoS2 has a direct band structure, the band gap width is 1.726 eV. It is found that MoS2 monolayer has a strong absorption of photons from visible light to the ultraviolet region, the maximum absorption coefficient of 1.98′105 cm-1. The analysis indicates that the single-layer MoS2 is suitable for the fabrication of microelectronic and optoelectronic devices, especially in the ultraviolet (UV) detector applications