A method for producing an electrical steel sheet, the method comprising: heating a slab having a chemical composition including by mass% C: 0.0050 % or less, Si: more than 3.5 % and 5.0 % or less, Mn: 0.10 % or less, Al: 0.0020 % or less, P: 0.030 % or less, N: 0.0040 % or less, S: 0.0005 % or more and 0.0030 % or less, and Ca: 0.0015 % or more and 0.01 % or less, and further at least one element selected from Sn: 0.01 % or more and 0.1 % or less, and Sb: 0.01 % or more and 0.1 % or less, and balance Fe and incidental impurities; then subjecting the slab to hot rolling consisting of rough rolling and finish rolling to obtain a hot rolled steel sheet; subjecting the steel sheet to subsequent hot band annealing and pickling; then subjecting the steel sheet to a single cold rolling to have a final sheet thickness; and then subjecting the steel sheet to final annealing to produce an electrical steel sheet, wherein a cumulative rolling reduction ratio in the rough rolling is 73.0 % or more, wherein in the hot band annealing, an annealing condition is selected that satisfies an area ratio of recrystallized grains in a cross section in a rolling direction of a steel sheet after the hot band annealing of 100 %, and a recrystallized grain size of 80 μm or more and 300 μm or less, under a condition where annealing temperature is 850 °C or higher and 1000 °C or lower, and annealing duration is 10 seconds or longer and 10 minutes or shorter, and wherein in the final annealing step, an annealing condition is selected that satisfies an area ratio of recrystallized grains in a cross section in the rolling direction of a steel sheet after the final annealing of 30 % or more and 95 % or less, and a length in the rolling direction of a connected non-recrystallized grain group of 2.5 mm or less, under a condition where annealing temperature is 670 °C or higher and 800 °C or lower, and annealing duration is 2 seconds or longer and 1 minute or shorter. heating a slab having a chemical composition including by mass% C: 0.0050 % or less, Si: more than 3.5 % and 5.0 % or less, Mn: 0.10 % or less, Al: 0.0020 % or less, P: 0.030 % or less, N: 0.0040 % or less, S: 0.0005 % or more and 0.0030 % or less, and Ca: 0.0015 % or more and 0.01 % or less, and further at least one element selected from Sn: 0.01 % or more and 0.1 % or less, and Sb: 0.01 % or more and 0.1 % or less, and balance Fe and incidental impurities; C: 0.0050 % or less, Si: more than 3.5 % and 5.0 % or less, Mn: 0.10 % or less, Al: 0.0020 % or less, P: 0.030 % or less, N: 0.0040 % or less, S: 0.0005 % or more and 0.0030 % or less, and Ca: 0.0015 % or more and 0.01 % or less, and further at least one element selected from Sn: 0.01 % or more and 0.1 % or less, and Sb: 0.01 % or more and 0.1 % or less, and balance Fe and incidental impurities; Sn: 0.01 % or more and 0.1 % or less, and Sb: 0.01 % or more and 0.1 % or less, and then subjecting the slab to hot rolling consisting of rough rolling and finish rolling to obtain a hot rolled steel sheet; subjecting the steel sheet to subsequent hot band annealing and pickling; then subjecting the steel sheet to a single cold rolling to have a final sheet thickness; and then subjecting the steel sheet to final annealing to produce an electrical steel sheet,