The present invention is directed to a solid electrolyte and a process for making the same for a sodium-sulfur secondary cell including a composition of 7.0 to 10.0 weight percent of Na.sub.2 O, 0.5 to 3.5 weight percent of MgO or 0.7 to 1.0 weight percent of Li.sub.2 O, 0.01 to 0.6 weight percent of WO.sub.3, and the balance of Al.sub.2 O.sub.3. The solid electrolyte is prepared by mixing Na.sub.2 O, MgO, Li.sub.2 O, WO.sub.3, and Al.sub.2 O.sub.3, calcining the resulting mixture, pulverizing the calcined body, and subjecting the resulting powders to sintering. Alternatively, the solid electrolyte is prepared by mixing Na.sub.2 O, MgO, or Li.sub.2 O, and Al.sub.2 O.sub.3 with one another, calcining the mixture, adding WO.sub.3 to the calcined body, pulverizing the resulting material, and subjecting the resulting powders to sintering.