In this work, A 2 Cu 3 In 3 Te 8 (A = Cd, Zn, Mn, Mg) thermoelectric chalcogenide materials, exhibiting intrinsically complex structures, low lattice thermal conductivities, high Seebeck coefficients, and thus promising thermoelectric properties, are designed and explored, by a systematic complex structure search surpassing the conventional doping and carrier concentration optimizing approach. The newly introduced alloying elements A (A = Cd, Zn, Mn, Mg) are found to uniformly distribute at the 4a and 4b sites which are solely occupied by Cu and In in the cation sublattice of A 2 Cu 3 In 3 Te 8 , leading to the strong cation disordering but surprisingly stable phase. The cation disordering preserves the high structure symmetry and enhances the phonon scattering, leading to reasonably good electrical transport properties coexisting with extremely low lattice thermal conductivities (as low as ∼0.32 W m −1 K −1 for Cd 2 Cu 3 In 3 Te 8 at 873 K). A peak thermoelectric figure of merit zT ∼ 0.9 at 873 K is achieved for Cd 2 Cu 3 In 3 Te 8 , which is one of the highest zT values for the pristine diamond-like compound. Also, a maximal average zT of 0.38 is obtained in the Cd 2 Cu 3 In 3 Te 8 sample, which is 54% higher than the value of prototype CuInTe 2 . Our results indicate that the A 2 Cu 3 In 3 Te 8 compound and its derivative I 4−x −III 4−x −A 2x −VI 8 (I = Cu, Ag; III = Al, Ga, In; A: divalent cations; VI = S, Se, Te; 0 < x < 4) are a promising family of thermoelectric materials with an intrinsically complex structure and low lattice thermal conductivity. KEYWORDS: A 2 Cu 3 In 3 Te 8 , thermoelectric materials, diamond-like structure, cation disordering, lattice thermal conductivity