The band structure and the optical properties of Ba0.5Sr0.5TiO3 are studied by the first principles method. The results show that the conduction band and the valence band are derived from the hybridization between titanium 3d orbitals and oxygen 2p orbitals. In the conduction band, titanium 3d orbitals play a primary role, while in the valence band, oxygen 2p orbitals play a primary role. The absorption coefficient is as targe as 105cm-1, and the absorption is mainly localised in the low energy region. The refractive index n（0） equals 2.1. Our results are in good agreement with the experimental results.