The electronic structure,densities of states and optical properties of the stable orthorhombic BaSi2 have been calculated using the first-principle density function theory and pseudopotential method. The results show that BaSi2 is an indirect semiconductor with the band gap of 1.086 eV,the valence bands of BaSi2 are mainly composed of Si 3p,3s and Ba 5d,and the conduction bands are mainly composed of Ba 6s,5d as well as Si 3p. The static dielectric function ε1(0) is 11.17,the reflectivity n0 is 3.35,and the biggest peak of the absorption coefficient is 2.15×105 cm-1. The results show that BaSi2 is an indirect semiconductor with the band gap of 1.086 eV, the valence bands of BaSi2 are mainly composed of Si 3p, 3s and Ba 5d, and the conduction bands are mainly composed of Ba 6s, 5d as well as Si 3p. The static dielectric function ε1 (0) is 11.17, the reflectivity n0 is 3.35, and the biggest peak of the absorption coefficient is 2.15 × 10 5 cm -1.