A production method for a grain-oriented electrical steel sheet, the method comprising: subjecting a steel slab to hot rolling, without re-heating or after re-heating, to obtain a hot rolled sheet, the steel slab having a composition consisting of, by mass% or mass ppm, C: 0.08 % or less, Si: 2.0 % to 4.5 %, Mn: 0.5 % or less, S: less than 50 ppm, Se: less than 50 ppm, O: less than 50 ppm, sol.Al: less than 100 ppm, N: 80 ppm or less, and optionally one or more of Ni: 0.005 % to 1.50 %, Sn: 0.01 % to 0.50 %, Sb: 0.005 % to 0.50 %, Cu: 0.01 % to 0.50 %, Cr: 0.01 % to 1.50 %, P: 0.0050 % to 0.50 %, Mo: 0.01 % to 0.50 % and Nb: 0.0005 % to 0.0100 %, and the balance being Fe and incidental impurities, and satisfying the relation of sol.Al (ppm) - N (ppm) × (26.98/14.00) ≤ 30 ppm; then subjecting the hot rolled sheet to annealing and rolling to obtain a cold rolled sheet of final sheet thickness; then subjecting the cold rolled sheet to nitriding treatment, with a nitrogen increase (ΔN) being specified by the following formula or, before, during or after primary recrystallization annealing; then applying an annealing separator on the cold rolled sheet; and subjecting the cold rolled sheet to secondary recrystallization annealing during which the staying time in a temperature range of 300°C to 800°C in the heating process is set to 5 hours or more to 150 hours or less: when sol.Al - N × (26.98/14.00) ≤ 0, 50 ppm ≤ ΔN ≤ 1000 ppm or when 0 < sol.Al - N × (26.98/14.00) ≤ 30, N − sol. Al × 14.00 / 26.98 + 100 ≤ ΔN ≤ N − sol. Al × 14.00 / 26.98 + 1000 subjecting a steel slab to hot rolling, without re-heating or after re-heating, to obtain a hot rolled sheet, the steel slab having a composition consisting of, by mass% or mass ppm, C: 0.08 % or less, Si: 2.0 % to 4.5 %, Mn: 0.5 % or less, S: less than 50 ppm, Se: less than 50 ppm, O: less than 50 ppm, sol.Al: less than 100 ppm, N: 80 ppm or less, and optionally one or more of Ni: 0.005 % to 1.50 %, Sn: 0.01 % to 0.50 %, Sb: 0.005 % to 0.50 %, Cu: 0.01 % to 0.50 %, Cr: 0.01 % to 1.50 %, P: 0.0050 % to 0.50 %, Mo: 0.01 % to 0.50 % and Nb: 0.0005 % to 0.0100 %, and the balance being Fe and incidental impurities, and satisfying the relation of sol.Al (ppm) - N (ppm) × (26.98/14.00) ≤ 30 ppm; then subjecting the hot rolled sheet to annealing and rolling to obtain a cold rolled sheet of final sheet thickness; then subjecting the cold rolled sheet to nitriding treatment, with a nitrogen increase (ΔN) being specified by the following formula or, before, during or after primary recrystallization annealing; then applying an annealing separator on the cold rolled sheet; and subjecting the cold rolled sheet to secondary recrystallization annealing during which the staying time in a temperature range of 300°C to 800°C in the heating process is set to 5 hours or more to 150 hours or less: when sol.Al - N × (26.98/14.00) ≤ 0, 50 ppm ≤ ΔN ≤ 1000 ppm or when 0 < sol.Al - N × (26.98/14.00) ≤ 30, N − sol. Al × 14.00 / 26.98 + 100 ≤ ΔN ≤ N − sol. Al × 14.00 / 26.98 + 1000 when sol.Al - N × (26.98/14.00) ≤ 0, 50 ppm ≤ ΔN ≤ 1000 ppm or when 0 < sol.Al - N × (26.98/14.00) ≤ 30, N − sol. Al × 14.00 / 26.98 + 100 ≤ ΔN ≤ N − sol. Al × 14.00 / 26.98 + 1000