Oxysulfide glasses in systems Li2S-B2O3(-LiBr) have been prepared and studied by differential scanning calorimetry and electrical measurement. In particular, the effects of Li2S as a modifier and LiBr as a dopant on glass transition temperature and conductivity of the glasses are studied. The results demonstrate that for the glasses of Li2S-B2O3 system when the Li2S content increases, both the glass transition temperature and activation energy of conduction increase, and reach a maximum in the range 30-33 mol% Li2S. The addition of LiBr decreases the glass transition temperature, but enhances pronouncedly the ionic conductivity of glasses. These results are discussed in reference to variation of the structural entities with the fraction of 4-coordinated borons in the glass.