High-throughput (HTP) material design is an emerging field and has been proved to be powerful in the prediction of novel functional materials. In this work, an HTP effort has been carried out for thermoelectric chalcogenides with diamond-like structures on the newly established Materials Informatics Platform (MIP). Specifically, the relaxation time evaluated by a reliable yet efficient method, which greatly improves the accuracy of HTP electrical transport calculations. The results show that all the compounds may have power factors over 10 mu W/cm.K-2 if fully optimized. A new series of diamond-like chalcogenides with an atomic ratio of 1:2:4 possess relatively higher electrical transport properties among all the compounds investigated. One particular compound, CdIn2Te4, and its variations have been verified experimentally with a peak ZT over 1.0. Further analysis reveals the existence of general conductive networks and the similar Pisarenko relations under the same anion sublattice, and the transport distribution function is found to be a good indicator for the power factors for the compounds investigated. This work demonstrates a successful case study in HTP material screening.