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.