We have measured the terahertz (THz) complex dielectric spectra of imidazolium ionic liquids by THz time-domain spectroscopy (THz-TDS) in the frequency range from 5 (0.15 THz) to 140 cm(-1) (4.2 THz). The ionic liquids investigated are 1-ethyl-3-methylimidazolium (EMIm(+))/trifluoromethanesulfonate (TfO-), EMIm(+)/tetrafluoroborate (BF4-), 1-butyl-3-methylimidazolium (BMIm(+))/TfO-, and BMIm(+)/BF4-. The dielectric values of the ionic liquids in the THz region are similar to those of short-chain alcohols. The THz dielectric values are related to subpicosecond-to-picosecond dynamics. The same trend has been observed in the empirical polarity E-T(30) although it is related to the static characteristics of polarity and hydrogen bonding ability. A difference between the two types of liquids is observed in the THz dielectric spectral shapes: the ionic liquids show structured lineshapes but short-chain alcohols show much less structured ones. The structured lineshapes of the ionic liquids reflect the low-frequency motions of interion and/or intramolecular vibrations. When the ionic liquids composed of the different imidazolium cations contain the same anions as counterions, their density-normalized THz dielectric spectra above 20 cm(-1) bear strong resemblance to each other in shape and magnitude. It shows clearly that the THz spectra do not originate from the intramolecular vibrations of the imodazolium cations. All of the intramolecular vibrations of the anions are located above 140 cm(-1) except the CF3-SO3 torsion of TfO-, the band of which alone cannot explain the broad THz dielectric spectra of the ionic liquids. Therefore, we conclude that the interion vibrations rather than the intramolecular vibrations dominantly contribute to the THz dielectric spectra. The results strongly indicate that even in the liquid phase the ionic liquids have local structures similar to their solid-phase structures.