A method of producing a grain-oriented electrical steel sheet, comprising: heating a steel slab in a temperature range of 1300 °C or less, the steel slab having a chemical composition containing, in mass%, C: 0.02 % or more and 0.08 % or less, Si: 2.0 % or more and 5.0 % or less, Mn: 0.02 % or more and 1.00 % or less, S and/or Se: 0.0015 % or more and 0.0100 % or less in total, N: less than 0.006 %, acid-soluble Al: less than 0.010 %, optionally %, one or more selected from Sn: 0.5 % or less, Sb: 0.5 % or less, Ni: 1.5 % or less, Cu: 1.5 % or less, Cr: 0.1 % or less, P: 0.5 % or less, Mo: 0.5 % or less, Ti: 0.1 % or less, Nb: 0.1 % or less, V: 0.1 % or less, B: 0.0025 % or less, Bi: 0.1 % or less, Te: 0.01 % or less, and Ta: 0.01 % or less, and a balance being Fe and inevitable impurities; subjecting the steel slab to hot rolling, to obtain a hot rolled steel sheet; optionally subjecting the hot rolled steel sheet to hot band annealing; subjecting the hot rolled steel sheet after the hot rolling or after the hot band annealing to cold rolling twice or more with intermediate annealing performed therebetween, to obtain a cold rolled steel sheet having a final sheet thickness; and subjecting the cold rolled steel sheet to primary recrystallization annealing with a rapid heating at 30°C/sec or more and 400 °C/sec or less in a range of 500 °C to 700 °C, then applying an annealing separator and then performing secondary recrystallization annealing, wherein in a heating process in final intermediate annealing, a temperature range in which heating is performed at a heating rate of 10 °C/s or less for 10 sec or more and 120 sec or less is provided in a temperature range from 700 °C to 950 °C. heating a steel slab in a temperature range of 1300 °C or less, the steel slab having a chemical composition containing, in mass%, C: 0.02 % or more and 0.08 % or less, Si: 2.0 % or more and 5.0 % or less, Mn: 0.02 % or more and 1.00 % or less, S and/or Se: 0.0015 % or more and 0.0100 % or less in total, N: less than 0.006 %, acid-soluble Al: less than 0.010 %, optionally %, one or more selected from Sn: 0.5 % or less, Sb: 0.5 % or less, Ni: 1.5 % or less, Cu: 1.5 % or less, Cr: 0.1 % or less, P: 0.5 % or less, Mo: 0.5 % or less, Ti: 0.1 % or less, Nb: 0.1 % or less, V: 0.1 % or less, B: 0.0025 % or less, Bi: 0.1 % or less, Te: 0.01 % or less, and Ta: 0.01 % or less, and a balance being Fe and inevitable impurities; C: 0.02 % or more and 0.08 % or less, Si: 2.0 % or more and 5.0 % or less, Mn: 0.02 % or more and 1.00 % or less, S and/or Se: 0.0015 % or more and 0.0100 % or less in total, N: less than 0.006 %, acid-soluble Al: less than 0.010 %, optionally %, one or more selected from Sn: 0.5 % or less, Sb: 0.5 % or less, Ni: 1.5 % or less, Cu: 1.5 % or less, Cr: 0.1 % or less, P: 0.5 % or less, Mo: 0.5 % or less, Ti: 0.1 % or less, Nb: 0.1 % or less, V: 0.1 % or less, B: 0.0025 % or less, Bi: 0.1 % or less, Te: 0.01 % or less, and Ta: 0.01 % or less, and a balance being Fe and inevitable impurities; subjecting the steel slab to hot rolling, to obtain a hot rolled steel sheet; optionally subjecting the hot rolled steel sheet to hot band annealing; subjecting the hot rolled steel sheet after the hot rolling or after the hot band annealing to cold rolling twice or more with intermediate annealing performed therebetween, to obtain a cold rolled steel sheet having a final sheet thickness; and subjecting the cold rolled steel sheet to primary recrystallization annealing with a rapid heating at 30°C/sec or more and 400 °C/sec or less in a range of 500 °C to 700 °C, then applying an annealing separator and then performing secondary recrystallization annealing, wherein in a heating process in final intermediate annealing, a temperature range in which heating is performed at a heating rate of 10 °C/s or less for 10 sec or more and 120 sec or less is provided in a temperature range from 700 °C to 950 °C. <EOS>