A beta-alumina solid electrolyte for use in a sodium-sulfur battery is composed of beta-alumina crystals having a degree of orientation toward the C axis thereof, of 0.2-0.4 and an aspect ratio of 4.0 or less. The beta-alumina solid electrolyte is composed of the beta-alumina crystals having a degree of orientation toward the C axis thereof, of 0.2-0.4 and has such a particle diameter distribution that the average particle diameter is 3 mum or less, the proportion of the particles having a particle diameter of 5 mum or less is 90% or more, and the maximum particle diameter is 300 mum or less. A process for producing a beta-alumina solid electrolyte using an alumina source material, a magnesium source material and a sodium source material, uses a magnesium-aluminum spinel as the magnesium source material and subjects all materials to mixing, granulation, molding and firing to obtain a beta-alumina solid electrolyte without subjecting the materials to calcination. The beta-alumina solid electrolyte has a low electrical resistance and a large strength to internal water pressure and exhibits excellent properties when used as a diaphragm for a sodium-sulfur battery.