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To understand the effects of Cd substitution for Cu, (Pb0.5Cu0.5-xCdx)Sr2(Ca0.7Y0.3)Cu2Oz (x = 0 ∼ 0.5) compounds were synthesized and the structural and superconducting properties of the compounds were characterized. Resistivity data revealed that superconducting transition temperature rises initially up to x = 0.25 and then decreases as the Cd doping content increases. Room-temperature thermoelectric power decreases at first up to x = 0.25 and then increases with higher Cd doping content, indicating that the change in Tc is mainly caused by the change in the hole concentration on the superconducting planes by the Cd doping. The non-monotonic dependence of the lattice parameters and the transition temperature with Cd doping content is discussed in connection with the possible formation of Pb+2 ions and the removal of excess oxygen caused by Cd substitution in the charge reservoir layer. A correlation between transition temperature and c/a lattice parameter ratio was observed for the (Pb0.5Cu0.5-xCdx)Sr2(Ca0.7Y0.3)Cu2Oz system.