ACu3Ti4O12 (A=Ca, Y or La) ceramic materials have been successively fabricated by using the solid-state reaction method. In the temperature range of 50—300 K, the dielectric characteristics of the samples are measured and the relationship among the AC conductivity, external frequency and temperature is analyzed. It has been found that if the relative content of Ca in the CaCu 3Ti4O12 crystals with identical components is greater than or equal to 0 776, the dielectric constant of the samples can reach the value of 104 For the ceramic compounds with a 3+ covalence in the `A' site such as La2/3 Cu3Ti4O12 and Y2/3Cu3Ti4O12, however, the dielec tric constant is only of the order of 103 Further analysis shows that the di electric constant of the ACu3Ti4O12 materials is mainly related to the number density of the barrier capacity in the samples. The relationship amo ng the conductivity, frequency and temperature depends on the combination of act ion of electrons, phonons and external field.