A circular cavity resonance method is improved to measure the frequency dependence of complex permittivity of a dielectric plate by using multimode TE0m1 with integer m. The measurement principle is based on a rigorous analysis by the Ritz-Galerkin method. A new circular cavity with lowered height is designed from a mode chart of a cavity to decrease the number of unwanted modes near the TE0m1 modes. A copper cavity having 20 GHz for the TE011 mode was constructed based on this design. For glass cloth PTFE, RT/duroid 6010 and FR-4 dielectric plates, the frequency dependences are measured from resonant frequencies for the TE0m1 (m = 1, 2, 3 ...) modes. These measured results agree well with ones measured by using the conventional four different size cavities with TE011 mode. It is verified that the designed cavity structure is useful to measure the frequency dependence of low loss dielectric plates.