Electronic structure, densities of states and optical properties of orthorhombic OsSi2 was calculated by the first-principle density function theory pseudopotential method. The calculated results show that OsSi2 is an indirect semiconductor with the band gap of 0.813 eV, the valence bands of OsSi2 are mainly composed of Os 5d and Si 3p, the conduction bands are mainly composed of Si 3p, 3s as well as Os 5d . The stastic dielectric function ε1（0） is 15.43, the reflectivity n0 is 3.93. Furthermore, the dielectric functions, refractivity index, reflectivity, absorption, conductivity and loss function of OsSi2 are analyzed in terms of the calculated band structure and densities of states. The results offer theoretical data for the design and application of OsSi2.