In a production of grain-oriented electrical steel sheet that is heated at a temperature of not higher than 1350°C, (a) the hot-rolled sheet is heated to a prescribed temperature of 1000°C to 1150°C, and after recrystallization is annealed for a required time at a lower temperature of 850°C to 1100°C, or (b) in the hot-rolled sheet annealing process decarburization is conducted to adjust the difference in the amount of carbon before and after decarburization to 0.002 to 0.02 mass%. In the temperature elevation process used in the decarburization annealing of the steel sheet, heating is conducted in the temperature range of 550°C to 720°C at a heating rate of at least 40°C/s, preferably 75 to 125°C/s, utilizing induction heating for the rapid heating used in the temperature elevation process in decarburization annealing.