In this article the conventional "solid-state reaction" method was used to synthesize perovskite Li_0.4Cd_0.6Ba₂Ca₂Cu₃O_10+δ. Four main types of compounds were obtained by physically replacing calcium oxide with cadmium in proportions 0, 0.03, 0.06 and 0.09, the pure Li_0.4Cd_0.6Ba₂Ca₂Cu₃O_10+δ phase, and the phases Li_0.4Cd_0.6Ba₂Ca_1.97Cd_0.03Cu₃O_10+δ and Li_0.4Cd_0.6Ba₂Ca_1.94Cd_0.06Cu₃O_10+δ and Li_0.4Cd_0.6Ba₂Ca_1.91Cd_0.09Cu₃O_10+δ ,respectively from mixing their constituent oxides and pressed into pelts and then sintered in the furnace at 850 degrees Celsius for 90 hours: These samples have been studied for their original dielectrically properties. The real dielectric constant, dielectric loss factor, and tangent were calculated in the frequency range (50 to 1000000 HZ). It was found that the partial substitution of cadmium oxide plays an important role in enhancing dielectrically properties.