Many superionic conducting glasses follow the Arrhenius type temperature dependence of ionic conductivity. However, in some superionic conductors it has been discovered that the conductivity deviate from the Arrhenius type behavior. In this paper, we present a simple model that describes the non-Arrhenius type ionic conductivity based on the Zwanzig model of diffusion. From the theory, the condition for the appearance of non-Arrhenius type ionic conductivity has been obtained.