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A new method for measuring complex permittivity of low-loss dielectric materials at millimeter-wave frequencies has been developed. The method uses a dielectric rod resonator excited by a nonradiative dielectric waveguide. Effective conductivity of conducting plates for short circuiting the resonator is determined by the difference of unloaded Q factors between TE0m1- and TE0mδ-mode resonators, made of the same low-loss dielectric material. The complex permittivity of the dielectric rod is determined by the resonant frequency (f0) and unloaded Q factor (Qu) of the TE0m1-mode resonator. The complex permittivities of single crystal sapphire, polycrystalline Ba(Mg12/W12/)O3 and Mg2Al4Si5O18 (cordierite) have been obtained at 60 and 77 GHz by the new method. These results were consistent with the values measured at microwave frequencies. It was also found that the frequency dependence of the dielectric loss tangent (tanδ) for sapphire can be expressed by frequency/tanδ=1×106 GHz.