A novel ternary antimonide Rb16Cd25.39(3)Sb36 has been synthesized by a solid-state reaction of the appropriate amount of elements in a welded niobium tube at 530 degrees C. The compound crystallizes in orthorhombic space group Cmcm (No. 63) with. a = 16.499(5) angstrom, b = 12.391(4) angstrom, c= 12.400(4) angstrom, and Z= 1. The structure features a new 3D network constructed of chains of Rb+-centered dodecahedra running along [001]. The atomic distribution of the Cd8Sb12 dodecahedron presents an energetically favored pattern without any Cd-Cd bonding. The formation of the phase and the occurrence of a very narrow phase width of Rb16Cd24+x,Sb-36 [0.94(2) <= x <= 1.47(3)] have been studied in detail. The Fermi level of the title compound is expected to be located between those of the hypothetical models of "[Rb16Cd24Sb36](0)" (I, poor metallic) and "[Rb16Cd24Sb36] + 4e" (II, narrow-band-gap semiconductor), which agrees well with the experimental measurements. In the temperature range of 300-473 K, the as-synthesized Rb16Cd25.39(3)Sb36 exhibits p-type semiconductor behavior and shows temperature-independent thermal conductivities (around 0.49 W/m-K). The electrical conductivity, Seebeck coefficient, and figure of merit (ZT) of Rb16Cd25.39(3)Sb36 are temperature-dependent; these values are 57.4 S/cm, +81.4 mu V/K, and 0.04, respectively, at 466 K.