The resonance property of the pair of left-handed metamaterial (LHM) and negative permittivity medium is analyzed in depth, and the results are applied to the design of an improved miniaturized cavity resonator (IMCR). The IMCR is numerically simulated, and the results show that the IMCR is resonant at 10.3GHz while its length and width is only 4.58 and 5.08mm, respectively, which are half that of the conventional one's. This research may contribute in theory to the miniaturization of resonance structures based on LHM.