Electronic and optical properties of Sr(Ti,Zr)O-3 crystals in the cubic (Pm-3m) and tetragonal (I4/mcm) phase were calculated by the first-principles calculations using the density functional theory and the local density approximation. The band structure of cubic and tetragonal phases show an indirect band gap at (R-I") point and at (M-I") point in the Brillouin zone, respectively. The linear photon-energy dependent dielectric functions and some optical properties such as the absorption coefficient, energy-loss function and reflectivity are calculated for both phases. The optical properties of tetragonal phase of Sr(Ti,Zr)O-3 were investigated by theoretical methods for the first time. We have also made some comparisons with the available related experimental and theoretical data.