A grain-oriented electromagnetic steel sheet is provided which has a low ratio of iron loss in a weaker magnetic field to that in a stronger magnetic field and has special advantage in EI cores and the like. Also provided is a process for producing that steel sheet. The grain-oriented electromagnetic steel sheet is characterized in that its crystal grains of important components are specified in terms of their proportions in number, and the contents of Al, Ti and B, with a forsterite film formed on a surface of the steel sheet. In the process a low-Al silicon slab is heated at below 1,250° C. before hot rolling and the hot-rolled sheet is annealed with a temperature rise in the range of from 5 to 25° C./sec and at a temperature of from about 800 to 1,000 for a period of time of shorter than about 100 seconds.