A method for manufacturing a grain-oriented electrical steel sheet, the method comprising: a step of heating a slab having a component composition containing, by mass %, C: 0.02% or more and 0.10% or less, Si: 2.5% or more and 4.5% or less, Mn: 0.01% or more and 0.15% or less, S and Se in total: 0.001% or more and 0.050% or less, acid-soluble Al: 0.01% or more and 0.05% or less, and N: 0.002% or more and 0.015% or less, optionally further containing one or more of Cu, Sn, Ni, Cr and/or Sb, wherein the amount of each of Cu, Sn, Ni, Cr and Sb may be 0.01% or more and 0.30% or less, with a remainder Fe and impurities to 1.280°C to 1.450°C and carrying out hot rolling to obtain a hot-rolled steel sheet; a step of, after carrying out hot-rolled steel sheet annealing on the hot-rolled steel sheet, carrying out cold rolling once or carrying out cold rolling twice or more with process annealing therebetween to obtain a cold-rolled steel sheet; a step of carrying out primary recrystallization annealing, id est rapid temperature increase and decarburization annealing, on the cold-rolled steel sheet; a step of applying an annealing separating agent including MgO to a surface of the cold-rolled steel sheet after the primary recrystallization annealing and then carrying out final annealing to obtain a final-annealed sheet wherein a forsterite coating is formed on the surface of the cold-rolled steel sheet; and a step of applying an insulating coating to the final-annealed sheet and then carrying out flattening annealing, wherein, in a temperature increase process for the primary recrystallization annealing, an average temperature increase velocity V, in °C/s, in a temperature range of 550°C to 700°C is 400 °C/s or more, T/L, in °C/mm, that is a ratio of an amount of temperature increased T, in °C, in a series of temperature increase processes, including a temperature increase in the temperature range of 550°C to 700°C, to a heated length L, in mm, of the series of temperature increase processes is 0.1 ≤ T/L ≤ 40, a tensile force S, in N/mm 2, imparted in a sheet travelling direction of the cold-rolled steel sheet is 1.96 ≤ S ≤ (19.6 - 1.96 x T/L), in the case of V ≤ 1,000, the tensile force S is 1.96 ≤ S ≤ (25.5 - 0.0137 x V), and, in the case of V > 1,000, the tensile force S is 1.96 ≤ S ≤ 11.8. a step of heating a slab having a component composition containing, by mass %, C: 0.02% or more and 0.10% or less, Si: 2.5% or more and 4.5% or less, Mn: 0.01% or more and 0.15% or less, S and Se in total: 0.001% or more and 0.050% or less, acid-soluble Al: 0.01% or more and 0.05% or less, and N: 0.002% or more and 0.015% or less, optionally further containing one or more of Cu, Sn, Ni, Cr and/or Sb, wherein the amount of each of Cu, Sn, Ni, Cr and Sb may be 0.01% or more and 0.30% or less, with a remainder Fe and impurities to 1.280°C to 1.450°C and carrying out hot rolling to obtain a hot-rolled steel sheet; a step of, after carrying out hot-rolled steel sheet annealing on the hot-rolled steel sheet, carrying out cold rolling once or carrying out cold rolling twice or more with process annealing therebetween to obtain a cold-rolled steel sheet; a step of carrying out primary recrystallization annealing, id est rapid temperature increase and decarburization annealing, on the cold-rolled steel sheet; a step of applying an annealing separating agent including MgO to a surface of the cold-rolled steel sheet after the primary recrystallization annealing and then carrying out final annealing to obtain a final-annealed sheet wherein a forsterite coating is formed on the surface of the cold-rolled steel sheet; and a step of applying an insulating coating to the final-annealed sheet and then carrying out flattening annealing, wherein, in a temperature increase process for the primary recrystallization annealing, an average temperature increase velocity V, in °C/s, in a temperature range of 550°C to 700°C is 400 °C/s or more, T/L, in °C/mm, that is a ratio of an amount of temperature increased T, in °C, in a series of temperature increase processes, including a temperature increase in the temperature range of 550°C to 700°C, to a heated length L, in mm, of the series of temperature increase processes is 0.1 ≤ T/L ≤ 40, a tensile force S, in N/mm 2, imparted in a sheet travelling direction of the cold-rolled steel sheet is 1.96 ≤ S ≤ (19.6 - 1.96 x T/L), in the case of V ≤ 1,000, the tensile force S is 1.96 ≤ S ≤ (25.5 - 0.0137 x V), and, in the case of V > 1,000, the tensile force S is 1.96 ≤ S ≤ 11.8.