A detailed experimental investigation of the current relaxation of α-LiIO3 single crystals is reported in this article. It was found that after turn off of the dc field initially applied in the direction of C-axis, the decrease of current follows a negative power law (t/t0)-α from the beginning responding time of our apparatus to a certain time tk, and after tk the current decreases approximately as (t/t0)(-α′ln(t/t0)). The parameters α,α′ and tk depend on the temperature of the specimen and the magnitude of the applied field.Nearly ten specimens were measured, with a small dc field the results obtained on most crystals show that the parameters α and α′ change from specimen to specimen but have their values within the following range:0.43≤α≤0.7, 0.07≤α′≤ 0.09. We also found that both the relaxation behavior of the apparent dielectric constant and that of neutron diffraction observed on α-LiIO3 conform to the same empirical expression as given above for the depolarization current except with different parameters. It may be concluded that these relaxation processes would be due to the same physical origin.