A method of producing a grain-oriented electrical steel sheet, comprising: heating a steel slab at 1300 °C or less, the steel slab having a chemical composition containing C: 0.002 mass% or more and 0.100 mass% or less, Si: 2.00 mass% or more and 6.50 mass% or less, Mn: 0.02 mass% or more and 1.00 mass% or less, S: 50 mass ppm or less, N: 50 mass ppm or less, Se: 50 mass ppm or less, acid-soluble Al: less than 100 mass ppm, and optionally one or more selected from Sb: 0.01 mass% or more and 0.50 mass% or less, Sn: 0.01 mass% or more and 0.50 mass% or less, Ni: 0.005 mass% or more and 1.5 mass% or less, Cu: 0.005 mass% or more and 1.5 mass% or less, Cr: 0.005 mass% or more and 0.1 mass% or less, P: 0.005 mass% or more and 0.5 mass% or less, Mo: 0.005 mass% or more and 0.5 mass% or less, Ti: 0.0005 mass% or more and 0.1 mass% or less, Nb: 0.0005 mass% or more and 0.1 mass% or less, and Bi: 0.005 mass% or more and 0.1 mass% or less; and a balance being Fe and inevitable impurities; subjecting the steel slab to hot rolling, to obtain a hot rolled steel sheet; subjecting the hot rolled steel sheet to hot band annealing; subjecting the hot rolled steel sheet after the hot band annealing to cold rolling once, or twice or more with intermediate annealing performed therebetween, to obtain a cold rolled steel sheet having a final sheet thickness; subjecting the cold rolled steel sheet to primary recrystallization annealing; and applying an annealing separator to a surface of the cold rolled steel sheet after the primary recrystallization annealing, and thereafter subjecting the cold rolled steel sheet to secondary recrystallization annealing, wherein in the hot band annealing, an average heating rate from ordinary temperature to 400 °C is set to 50 °C/s or more and 500 °C/s or less, and a time to reach 900 °C from 400 °C is set to 10 sec or more and 100 sec or less. heating a steel slab at 1300 °C or less, the steel slab having a chemical composition containing C: 0.002 mass% or more and 0.100 mass% or less, Si: 2.00 mass% or more and 6.50 mass% or less, Mn: 0.02 mass% or more and 1.00 mass% or less, S: 50 mass ppm or less, N: 50 mass ppm or less, Se: 50 mass ppm or less, acid-soluble Al: less than 100 mass ppm, and optionally one or more selected from Sb: 0.01 mass% or more and 0.50 mass% or less, Sn: 0.01 mass% or more and 0.50 mass% or less, Ni: 0.005 mass% or more and 1.5 mass% or less, Cu: 0.005 mass% or more and 1.5 mass% or less, Cr: 0.005 mass% or more and 0.1 mass% or less, P: 0.005 mass% or more and 0.5 mass% or less, Mo: 0.005 mass% or more and 0.5 mass% or less, Ti: 0.0005 mass% or more and 0.1 mass% or less, Nb: 0.0005 mass% or more and 0.1 mass% or less, and Bi: 0.005 mass% or more and 0.1 mass% or less; and a balance being Fe and inevitable impurities; C: 0.002 mass% or more and 0.100 mass% or less, Si: 2.00 mass% or more and 6.50 mass% or less, Mn: 0.02 mass% or more and 1.00 mass% or less, S: 50 mass ppm or less, N: 50 mass ppm or less, Se: 50 mass ppm or less, acid-soluble Al: less than 100 mass ppm, and optionally one or more selected from Sb: 0.01 mass% or more and 0.50 mass% or less, Sn: 0.01 mass% or more and 0.50 mass% or less, Ni: 0.005 mass% or more and 1.5 mass% or less, Cu: 0.005 mass% or more and 1.5 mass% or less, Cr: 0.005 mass% or more and 0.1 mass% or less, P: 0.005 mass% or more and 0.5 mass% or less, Mo: 0.005 mass% or more and 0.5 mass% or less, Ti: 0.0005 mass% or more and 0.1 mass% or less, Nb: 0.0005 mass% or more and 0.1 mass% or less, and Bi: 0.005 mass% or more and 0.1 mass% or less; and a balance being Fe and inevitable impurities; subjecting the steel slab to hot rolling, to obtain a hot rolled steel sheet; subjecting the hot rolled steel sheet to hot band annealing; subjecting the hot rolled steel sheet after the hot band annealing to cold rolling once, or twice or more with intermediate annealing performed therebetween, to obtain a cold rolled steel sheet having a final sheet thickness; subjecting the cold rolled steel sheet to primary recrystallization annealing; and applying an annealing separator to a surface of the cold rolled steel sheet after the primary recrystallization annealing, and thereafter subjecting the cold rolled steel sheet to secondary recrystallization annealing, wherein in the hot band annealing, an average heating rate from ordinary temperature to 400 °C is set to 50 °C/s or more and 500 °C/s or less, and a time to reach 900 °C from 400 °C is set to 10 sec or more and 100 sec or less.