Several Na-S solid phases have been considered to be produced in low-temperature Na/S batteries during chargedischarge reactions. We study structural and electronic properties of ¡-S and Na 2 S x (x = 1, 2, 4, and 5) crystals using first-principles calculations. Calculated structural properties are in good agreement with experiments, and the van der Waals interactions have an essential role on the cohesive properties in ¡-S. The results of energetics and electronic structures show that all the calculated Na-S crystal phases are insulating and are stable relative to the elemental Na and S phases. We estimate voltage curves as a function of the Na concentration in the S-cathode of all-solid Na/S batteries, showing mainly three voltage regions at 2.