The optical band gap energy for $SrTiO_3$ by reduction at high temperature was 3.15 eV. The reflectivity of reduced $SrTiO_3$ single crystals showed little variation, however, the reflectivity by the reduction condition had no effect. For the phonon mode at about 790 $cm^{-1}$, a blue-shift took place upon $N_2$ reduction and the decreased. However, a red-shift took place upon a $H_2-N_2$ reduction and the increased at the same phonon mode. With decreasing temperature the dielectric constant decreased rapidly. The thermal activation energies were 0.92-1.02 eV.