We have systematically grown and characterized (Bi, Pb)2Sr2CaCu2Oy (BPSCCO) single crystals, and investigated the tunneling properties and the intrinsic Josephson effects of the single crystals as a function of the nominal composition of Pb, x. It was observed that Pb atoms (ions) were monotonically substituted for Bi atoms (ions) in the (Bi, Pb)-O layers of the crystals with increasing x in a region of 0x0.5, while the modulation structure was maintained in a range of 0x0.3, but disappeared in x0.3, accompanying the decrease of c-lattice parameter and Tc. Moreover, it was found that the energy gaps Δ of BPSCCO depend hardly on x for x0.5, which are about 24 meV, so that the Pb-induced electronic change in the (Bi, Pb)-O layer do not perturb the electronic states in this superconducting system. And it was confirmed that the currentvoltage characteristics of the BPSCCO single crystals had multiple resistive branches corresponding to a series array of several hundreds Josephson junctions, and showed Shapiro steps and zero-crossing steps with the voltage separation of the order of mV resulting from the phase locking of about a hundred Josephson junctions among them under microwave irradiation. The estimated number of junctions gave the concept that the intrinsic Josephson junctions consist of the superconducting block layers and the insulating layers in the BPSCCO single crystals.