Copper-based sulfide semiconductors with the structure based on a sphalerite-like network can provide environmentally sound solutions to thermoelectric and photovoltaic energy conversion at a low cost. In this study, we report the synthesis and characterization of a copper-based sulfide, Cu30Ti6Sb2S32, discovered within the pseudobinary Cu3SbS4-Cu4TiS4 system. This new compound crystallizes in a colusite-like cubic structure, which is characterized by “interstitial” Ti atoms forming tetrahedral-octahedral [TiS4]Cu6 complexes linearly arranged within the Cu-S corner-sharing matrix. The [TiS4]Cu6 unit arrangement distinguishes the crystal structures of Cu26Ti2Sb6S32 (isolated units, 0D linkage), Cu30Ti6Sb2S32 (chain of linked units, 1D), and Cu4TiS4 (plane of linked units, 2D). We emphasize the semiconducting nature and the low thermal conductivity. The electronic structure and vibrational properties are investigated by the combination of experiments and first-principles calculations. We demonstrate that a design approach based on the pseudobinary composition, here, with the generic formula (Cu3SbS4)1-x(Cu4TiS4)x, is a fruitful direction for the discovery of new copper-based sulfides with tunable transport properties.