The characteristic curves, measured with a 10 kHz signal of the apparent dielectric constants ε′c and ε′a were obtained for a bias electrostatic potential of various voltages applied on an α-LiIO3 single crystal z-cut plate, the potential being either in the homogeneous or in the heterogeneous direction relative to the crystal's electrical polarity. Results show that there do not exist Schottky barrier layers in the crystal. A relaxation phenomen on of ε′c as the result of application of the bias d-c field was observed similar to that which had been detected in the case of the enhancement of neutron diffraction. It was experimentally verified that the current carriers in this crystal are chiefly, if not entirely, lithium ions, and that the conductivity may be approximately described as one-dimensional along the c-axis. The characteristic curves of ρc against V+ (homogeneous direction) and V-(heterogeneous) were also obtained.