The present invention provides 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 SiO2, Al2O3, B2O3, MgO, CaO, SrO and BaO and containing substantially no alkali metal oxide, of which the temperature at which the viscosity becomes 10<2 >dPa.s, is at most 1,600 DEG C. and which contains sulfur in an amount of from 0.001 to 0.1% as calculated as SO3, 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 SO3, as represented by the mass percentage, per 100% of the total amount of the above matrix composition.