The invention provides an alkali-free glass substrate small in the variation of the thermal shrinkage and a process for producing the same. An alkali-free glass substrate of the invention has an absolute value of a thermal shrinkage of 50 ppm or more when the alkali-free glass substrate is heated at a rate of 10° C./min from a room temperature, kept at a holding temperature of 450° C. for 10 hr and then cooled at a rate of 10° C./min.