Search for new thermal barrier materials with high-temperature stability is very difficult because there are intractable choices among thousands of possible candidates. The present paper shows that identifying and developing new low thermal conductivity materials can be accomplished by first-principles calculations of equilibrium crystal structure and elasticity, and thereafter making theoretical prediction of minimum high-temperature lattice thermal conductivity basing on David Clarke's method for insulating materials. We highlight a new oxynitride ceramic, Y4Si2O7N2, with a low theoretical minimum thermal conductivity of 1.12 W·m−1·K−1. The theoretical result is further validated by experimental measurement of thermal conductivity of dense and bulk Y4Si2O7N2. The experimental thermal conductivity is 1.50 W·m−1·K−1 at 1300 K. Furthermore, thermal properties of Y4Si2O7N2 are investigated for evaluating its potential performances.