A process for producing a grain-oriented magnetic steel sheet in which slab heating is conducted at a temperature of 1,350°C or lower and the annealing of a hot-rolled sheet is conducted: (a) in a step in which the hot-rolled sheet is heated to a given temperature of 1,000-1,150°C to cause recrystallization and then annealed at a temperature of 850-1,100°C lower than that temperature or (b) by decarburizing the hot-rolled sheet during annealing so that the difference in carbon content between the steel sheet before the annealing and that after the annealing is 0.002-0.02 mass% and the heating in the decarburization/annealing is conducted under such conditions that the heating rate during the period when the temperature of the steel sheet is in the range of 550-720°C is 40 °C/sec or higher, preferably 75-125 °C/sec. Induction heating is used for the rapid heating in the heating step in the decarburization/annealing.