A method of producing a grain oriented electrical steel sheet, the method comprising: heating a steel slab having a composition containing by mass% C: 0.0005 % to 0.005 %, Si: 2.0 % to 4.5 %, Mn: 0.005 % to 0.3 %, S and/or Se (in total): 0.05 % or less, sol.Al: 0.010 % to 0.04 %, N: 0.005 % or less, optionally one or more elements selected from Ni: 0.005 % to 1.5 %, Sn: 0.005 % to 0.50 %, Sb: 0.005 % to 0.50 %, Cu: 0.005 % to 1.5 %, Cr: 0.005 % to 0.10 %, P: 0.005 % to 0.50 %, and Mo: 0.005 % to 0.50 %, optionally one or more elements selected from Ti: 0.001 % to 0.1 %, Nb: 0.001 % to 0.1 %, and V: 0.001 % to 0.1 %, and the balance being Fe and incidental impurities; then subjecting the slab to hot rolling to obtain a hot rolled sheet; then optionally subjecting the hot rolled sheet to hot band annealing under the conditions of soaking temperature: 800 °C or higher and 1200 °C or lower, soaking time: 2 seconds or more and 300 seconds or less; then subjecting the hot rolled and optionally hot band annealed sheet to cold rolling once, or twice or more with intermediate annealing at a soaking temperature of 800 °C or higher and 1200 °C or lower, and for a soaking time of 2 seconds or more and 300 seconds or less performed therebetween to obtain a cold rolled sheet with final sheet thickness; and then subjecting the cold rolled sheet to primary recrystallization annealing at a soaking temperature of 700 °C or higher and 1000 °C or lower; then subjecting the cold rolled sheet to secondary recrystallization annealing, wherein the hot band annealing is carried out when the intermediate annealing is not performed, a solute C content parameter X calculated from the following formula is used, and an average cooling rate R (°C/s) between 800 °C and 200 °C after a heating process right before final cold rolling is set to equal to or lower than an upper limit average cooling rate R H calculated from the following formula to achieve an aging index AI of the steel sheet before the final cold rolling of 70 MPa or less, X = % Si / 28.09 + 100 % C / 12.01 R H = 10 / X where [%M] in formula represents the content of element M (mass%), and wherein an average heating rate between 500 °C and 700 °C in the primary recrystallization annealing is adjusted to 10 °C/s or higher and 100 °C/s or lower to achieve a ratio of <225> intensity to random intensity of 12 or more and a ratio of <225> intensity to <110> intensity of 7 or more in a texture of a center layer in the sheet thickness direction of the steel sheet subjected to primary recrystallization annealing. heating a steel slab having a composition containing by mass% C: 0.0005 % to 0.005 %, Si: 2.0 % to 4.5 %, Mn: 0.005 % to 0.3 %, S and/or Se (in total): 0.05 % or less, sol.Al: 0.010 % to 0.04 %, N: 0.005 % or less, optionally one or more elements selected from Ni: 0.005 % to 1.5 %, Sn: 0.005 % to 0.50 %, Sb: 0.005 % to 0.50 %, Cu: 0.005 % to 1.5 %, Cr: 0.005 % to 0.10 %, P: 0.005 % to 0.50 %, and Mo: 0.005 % to 0.50 %, optionally one or more elements selected from Ti: 0.001 % to 0.1 %, Nb: 0.001 % to 0.1 %, and V: 0.001 % to 0.1 %, and the balance being Fe and incidental impurities; C: 0.0005 % to 0.005 %, Si: 2.0 % to 4.5 %, Mn: 0.005 % to 0.3 %, S and/or Se (in total): 0.05 % or less, sol.Al: 0.010 % to 0.04 %, N: 0.005 % or less, optionally one or more elements selected from Ni: 0.005 % to 1.5 %, Sn: 0.005 % to 0.50 %, Sb: 0.005 % to 0.50 %, Cu: 0.005 % to 1.5 %, Cr: 0.005 % to 0.10 %, P: 0.005 % to 0.50 %, and Mo: 0.005 % to 0.50 %, optionally one or more elements selected from Ti: 0.001 % to 0.1 %, Nb: 0.001 % to 0.1 %, and V: 0.001 % to 0.1 %, and the balance being Fe and incidental impurities; then subjecting the slab to hot rolling to obtain a hot rolled sheet; then optionally subjecting the hot rolled sheet to hot band annealing under the conditions of soaking temperature: 800 °C or higher and 1200 °C or lower, soaking time: 2 seconds or more and 300 seconds or less; then subjecting the hot rolled and optionally hot band annealed sheet to cold rolling once, or twice or more with intermediate annealing at a soaking temperature of 800 °C or higher and 1200 °C or lower, and for a soaking time of 2 seconds or more and 300 seconds or less performed therebetween to obtain a cold rolled sheet with final sheet thickness; and then subjecting the cold rolled sheet to primary recrystallization annealing at a soaking temperature of 700 °C or higher and 1000 °C or lower; then subjecting the cold rolled sheet to secondary recrystallization annealing, wherein the hot band annealing is carried out when the intermediate annealing is not performed, a solute C content parameter X calculated from the following formula is used, and an average cooling rate R (°C/s) between 800 °C and 200 °C after a heating process right before final cold rolling is set to equal to or lower than an upper limit average cooling rate R H calculated from the following formula to achieve an aging index AI of the steel sheet before the final cold rolling of 70 MPa or less, X = % Si / 28.09 + 100 % C / 12.01 R H = 10 / X where [%M] in formula represents the content of element M (mass%), and wherein an average heating rate between 500 °C and 700 °C in the primary recrystallization annealing is adjusted to 10 °C/s or higher and 100 °C/s or lower to achieve a ratio of <225> intensity to random intensity of 12 or more and a ratio of <225> intensity to <110> intensity of 7 or more in a texture of a center layer in the sheet thickness direction of the steel sheet subjected to primary recrystallization annealing.