Using first-principles simulations, we predict a high-performance solid electrolyte with composition Na 10 GeP 2 S 12 for use in sodium-sulfur (Na-S) batteries. The thermodynamic stability of its structure is established through determination of decomposition reaction energies and phonons, while Na-ionic conductivity is obtained using ab initio molecular dynamics at elevated temperatures. Our estimate of the room-temperature (RT) conductivity is 4.7 Â 10 À3 S cm À1 , which is slightly higher than those of other superionic solid electrolytes such as b 00 -alumina and Na 3 Zr 2 Si 2 PO 12 , currently used in practical hightemperature Na-S batteries. Activation energy obtained from the Arrhenius plot (in the range 800-1400 K) is 0.2 eV, which is slightly lower than the typical values exhibited by other ceramic conductors (0.25-1 V) (Hueso et al., Energy Environ. Sci., 2013, 6, 734). We show that soft Na-S phonon modes are responsible for its thermodynamic stability and the lower activation barrier for diffusion of Na-ions.Finally, the calculated electronic bandgap of 2.7 eV (a wide electrochemical window) augurs well for its safe use in sodium batteries. Opening up a possibility for realizing RT operation of Na-S batteries, our prediction of a new phase in the Na-Ge-P-S system will stimulate experimental studies of the material.