Samples of ($Bi_{2-x}Sb_x)PbSr_2Ca_2Cu_3O_y$, compositions with x=0.0, 0.1, and 0.2 were prepared by solid-state reaction. The solubility of Sb into the 2223 phase is lower than 0.05 for the ratio of Sb/Bi. The lack of stability of the Sb-substituted $Bi_2O_2$ double layers is likely to cause the solubility low. There is no great dependence of lattice parameters on the Sb-content, and bonds around the square-pyramidal Cu atom are not affected by the $Sb^{3+}$ ion substituted. The superconducting transition temperature of this system is decreased gradually with increase of Sb, which is tentatively attributable to the perturbation of the Bi 6p-O 2p band and/or to the low volume fraction of the 2223 phase.