A new compound of Cu 5 AlSn 2 S 8 , which contained earth-abundant and environment-friendly elements and had a diamond-like crystal structure, was designed, and its electronic structure and thermoelectric transport properties from 300 K to 700 K were investigated by first-principles calculations, Boltzmann transport equations, and a modified Slack's model. The largest power factors of Cu 5 AlSn 2 S 8 at 700 K were 47.5 9 10 10 W m À1 K À2 s À1 and 14.7 9 10 10 W m À1 K À2 s À1 for p-and n-type semiconductors, respectively. The lattice thermal conductivity of Cu 5 AlSn 2 S 8 was calculated with its shear modulus and isothermal bulk modulus, which were also obtained by first-principles calculations. The lattice thermal conductivity was 0.9-2.2 W m À1 K À1 from 300 K to 700 K, relatively low among thermoelectric compounds. This theoretical study showed that Cu 5 AlSn 2 S 8 could be a potential thermoelectric material.