To provide an alkali free glass which is suitable as a glass substrate for LCD and has few defects of bubbles and an undissolved starting material, and a process for producing an alkali free glass which can readily lower the defects in bubbles and an undissolved starting material.An alkali free glass with a matrix composition comprising SiO.sub.2, Al.sub.2O.sub.3, B.sub.2O.sub.3, MgO, CaO, SrO and BaO and containing substantially no alkali metal oxide, of which the temperature at which the viscosity becomes 10.sup.2 dPas, is at most 1,600.degree. C. and which contains sulfur in an amount of from 0.001 to 0.1% as calculated as SO.sub.3, as represented by the mass percentage, per 100% of the total amount of the above matrix composition, and a process for producing a glass which comprises preparing a starting material and melting it so that a sulfate be incorporated to the starting material in an amount of from 0.01 to 5% as calculated as SO.sub.3, as represented by the mass percentage, per 100% of the total amount of the above matrix composition.