High-entropy compounds with compositional complexity can be designed as new thermoelectric materials. Here a data-driven model was developed, which chose suitable elements to reduce the enthalpy of formation and hence to increase the chance of single phase formation. Using this model, two high-entropy sulfides were designed, metallic Cu5SnMgGeZnS9 and semiconducting Cu3SnMgInZnS7. They were then successfully fabricated as single-phase dense ceramics with homogeneously distributed cations, and their phase stability and atomic local structures were investigated using density functional theory calculations. Finally, a zT value of 0.58 at 773 K was obtained for Cu5Sn1.2MgGeZnS9, where additional Sn was used to tune the carrier concentration. This work provides a simple approach to find new high-entropy functional materials in the largely unexplored multielement chemical space.