By using the Debye-Hückel equation and the Poisson equation, the almost one-dimensional ionic conductive behaviors of α-LiIO3 have been analysed theoretically. The current across the boundaries between the crystal and metallic electrodes is con-sidered to be limited by rate processes. The asymmetry of the ± c-directions due to spontaneous polarization of the crystal has been taken into consideration. The explicit expression derived for the apparent DC conductivity is satisfactory in explaining the characteristic behavior of α-LiIO3, e.g., the dependence of conductivity on applied voltage, as shown experimentally in 1. The functional relationship between the AC dielectric constant and the bias field (cf. 1) is interpreted partially by following the approach given in 2. It is also pointed out that the weak current constantly flowing through the wire connecting the end surfaces of opposite polarity of an α-LiIO3 single crystal (cf. 3), as well as similar phenomena observed in our own laboratory on poled ferroelectrics such as BaxSr1-xNb2O6(x～1/3), are caused by the crystal-line polarity EMF. This EMF coexists with the spontaneous, polarization Ps.