The electronic and optical properties of the lead sulfide are studied using first-principles calculations. The energy band structure and density of state of PbS are calculated. The results suggest that PbS exhibit a narrow band gap. The Mulliken analysis shows that the Pb-S bond is ionic. The dielectric function, absorption coefficient, reflectivity spectrum, refractive index and extinction coefficient are calculated for radiation up to 35eV. We have show that S (3p) electrons states and Pb (6p) electrons states play an important role in these transitions.