A method for manufacturing a grain oriented electrical steel sheet, the method comprising: subjecting a slab having the composition consisting of: in terms of % by mass C: 0.08% or less, Si; 2.0 to 8.0%, Mn: 0.005 to 1.0%, and either A) or B): A) at least one type of inhibitor selected from AlN, MnS and MnSe, in which, if one of the selected inhibitors is AIN, the composition further consists of Al: 0.01% to 0.065% and N: 0.005% to 0.012%, and if one of the selected inhibitors is MnS, the composition further consists of S: 0.005% to 0.03%, and if one of the selected inhibitors is MnSe, the composition further consists of Se: 0.005% to 0.03%, B) Al: 100 mass ppm or less, N: 50 mass ppm or less, S: 50 mass ppm or less, and Se: 50 mass ppm or less, and optionally at least one element selected from Ni: 0.03 to 1.50%, Sn: 0.01 to 1.50%, Sb: 0.005 to 1.50%, Cu: 0.03 to 3.0%, P: 0.03 to 0.50%, Mo: 0.005 to 0.10%, and Cr: 0.03 to 1.50% with a balance being Fe and incidental impurities, to hot rolling to obtain a hot-rolled steel sheet; then, subjecting the steel sheet to hot band annealing within a temperature range of 800°C to 1100°C; subjecting the steel sheet to subsequent cold rolling once, or twice or more with intermediate annealing performed therebetween, to be finished to a final sheet thickness; subjecting the steel sheet to subsequent decarburization; then applying an annealing separator mainly composed of MgO to a surface of the steel sheet before subjecting the steel sheet to final annealing; and subjecting the steel sheet to subsequent tension coating, wherein linear grooves are formed in a widthwise direction of the steel sheet by electrolytic etching before the final annealing for forming a forsterite film, an average cooling rate within a temperature range of at least 750°C to 350°C is 40°C/s or higher during cooling at the time of the hot band annealing, an average heating rate within a temperature range of at least 500°C to 700°C is controlled to be 50°C/s or higher during heating at the time of the decarburization, and the final annealing is performed on the steel sheet in the form of a coil having a diameter within a range of 500 mm to 1500 mm. subjecting a slab having the composition consisting of: in terms of % by mass C: 0.08% or less, Si; 2.0 to 8.0%, Mn: 0.005 to 1.0%, and either A) or B): A) at least one type of inhibitor selected from AlN, MnS and MnSe, in which, if one of the selected inhibitors is AIN, the composition further consists of Al: 0.01% to 0.065% and N: 0.005% to 0.012%, and if one of the selected inhibitors is MnS, the composition further consists of S: 0.005% to 0.03%, and if one of the selected inhibitors is MnSe, the composition further consists of Se: 0.005% to 0.03%, B) Al: 100 mass ppm or less, N: 50 mass ppm or less, S: 50 mass ppm or less, and Se: 50 mass ppm or less, and optionally at least one element selected from Ni: 0.03 to 1.50%, Sn: 0.01 to 1.50%, Sb: 0.005 to 1.50%, Cu: 0.03 to 3.0%, P: 0.03 to 0.50%, Mo: 0.005 to 0.10%, and Cr: 0.03 to 1.50% with a balance being Fe and incidental impurities, to hot rolling to obtain a hot-rolled steel sheet; A) at least one type of inhibitor selected from AlN, MnS and MnSe, in which, if one of the selected inhibitors is AIN, the composition further consists of Al: 0.01% to 0.065% and N: 0.005% to 0.012%, and if one of the selected inhibitors is MnS, the composition further consists of S: 0.005% to 0.03%, and if one of the selected inhibitors is MnSe, the composition further consists of Se: 0.005% to 0.03%, B) Al: 100 mass ppm or less, N: 50 mass ppm or less, S: 50 mass ppm or less, and Se: 50 mass ppm or less, and optionally at least one element selected from Ni: 0.03 to 1.50%, Sn: 0.01 to 1.50%, Sb: 0.005 to 1.50%, Cu: 0.03 to 3.0%, P: 0.03 to 0.50%, Mo: 0.005 to 0.10%, and Cr: 0.03 to 1.50% with a balance being Fe and incidental impurities, to hot rolling to obtain a hot-rolled steel sheet; then, subjecting the steel sheet to hot band annealing within a temperature range of 800°C to 1100°C; subjecting the steel sheet to subsequent cold rolling once, or twice or more with intermediate annealing performed therebetween, to be finished to a final sheet thickness; subjecting the steel sheet to subsequent decarburization; then applying an annealing separator mainly composed of MgO to a surface of the steel sheet before subjecting the steel sheet to final annealing; and subjecting the steel sheet to subsequent tension coating, wherein linear grooves are formed in a widthwise direction of the steel sheet by electrolytic etching before the final annealing for forming a forsterite film, an average cooling rate within a temperature range of at least 750°C to 350°C is 40°C/s or higher during cooling at the time of the hot band annealing, an average heating rate within a temperature range of at least 500°C to 700°C is controlled to be 50°C/s or higher during heating at the time of the decarburization, and the final annealing is performed on the steel sheet in the form of a coil having a diameter within a range of 500 mm to 1500 mm. linear grooves are formed in a widthwise direction of the steel sheet by electrolytic etching before the final annealing for forming a forsterite film, an average cooling rate within a temperature range of at least 750°C to 350°C is 40°C/s or higher during cooling at the time of the hot band annealing, an average heating rate within a temperature range of at least 500°C to 700°C is controlled to be 50°C/s or higher during heating at the time of the decarburization, and the final annealing is performed on the steel sheet in the form of a coil having a diameter within a range of 500 mm to 1500 mm.