Experimental measurements clearly reveal the presence of bulk superconductivity in the CsPbxBi4-xTe6 (0.3=<x=<1.0) materials, i.e. the first member of the thermoelectric series of Cs[PbmBi3Te5+m], these materials have the layered orthorhombic structure containing infinite anionic [PbBi3Te6]- slabs separated with Cs+ cations. Temperature dependences of electrical resistivity, magnetic susceptibility, and specific heat have consistently demonstrated that the superconducting transition in CsPb0.3Bi3.7Te6 occurs at Tc=3.1K, with a superconducting volume fraction close to 100% at 1.8 K. Structural study using aberration-corrected STEM/TEM reveals a rich variety of microstructural phenomena in correlation with the Pb-ordering and chemical inhomogeneity. The superconducting material CsPb0.3Bi3.7Te6 with the highest Tc shows a clear ordered structure with a modulation wave vector of q=a*/2+ c*/1.35 on the a-c plane. Our study evidently demonstrates that superconductivity deriving upon doping of narrow-gap semiconductor is a viable approach for exploration of novel superconductors.