In this work, we investigate the far-infrared wave properties for a ferroelectric material, i.e., lithium tantalate (LiTaO3), in the double-negative region, i.e., both the real parts of permittivity and permeability are negative. The analysis has been done based on the calculated surface impedances for three model structures, i.e., material occupying semi-infinite space (structure I), material of a slab immersed in free space (structure II), and a layered structure made of film on a dielectric substrate (structure III). It is found that the surface impedance spectrum exhibits resonant behavior. In structure I, there are only two resonant points, which arise mainly from the pole of permeability and the zero of permittivity. In structure II, multiple resonances can be found, and they strongly rely on the film thickness. Finally, we specifically investigate the substrate resonant phenomenon in structure III.