The electrical conductivity and thermoelectric power of the superionic conductor Ag3SBr were measured in the temperature range from 293 K to 493 K. Considerable deviations from the Arrhenius law was observed in the results of the ionic conductivity. The temperature dependence of the thermoelectric power of this system was found to be very different from that in other superionic conductors. The electrical conductivity measurements were also made down to 93 K; a discontinuous change was observed near 133 K, corresponding to the β-γ phase transition. A model theory of ionic conduction is proposed, in which characteristic features of the crystal structure are taken into account. The experimental results of this system appear to be interpreted qualitatively in terms of this model.