The polymorphism and anisotropy of electrical, dielectric, and thermophysical properties of "pure" and doped LiIO3 single crystals are studied. The hexagonal alpha-LiIO3 phase is a 1-D ionic conductor (along the c axis). The anisotropy of the ionic conductivity of the alpha-phase can be reduced by doping with transitive metals (Fe, Mo, Ni). The martensitic character of the alpha <->gamma transition is proved. In the gamma-phase, only a slight anisotropy of the conductivity is found. The alpha <->gamma transition is not an ionic-superionic one.