Based on the characteristics of superionic glasses and a physical picture of unified theory of the low-frequency fluctuation, dissipation and relaxation phenomenon, the transport features of a non-Markovian process of conduct ions are explored. The theory predict that the frequency independent conductance follows a simple Arrhenius type dependence on temperature at high temperatures, The theory can also explain the frequency dispersion of the conductance at low temperatures, and the degree of the frequency dispersion depends on the infrared divergence exponent n.