A method provides a slab by continuous casting of a steel having a component composition of, in mass %, C: 0.005% or less, Mn: 0.05 to 0.5%, Al: 0.01 to 0.10%, N: 0.0010 to 0.0070%, B: 0.15×N to 0.75×N (0.15 to 0.75 in terms of B/N), and one or both of Nb: 4×C to 20×C (4 to 20 in terms of Nb/C) and Ti: 2×C to 10×C (2 to 10 in terms of Ti/C), and the balance of Fe and inevitable impurity elements; rough rolling the slab; finish rolling the rough-rolled slab wherein 5% or more and less than 50% of the total amount of rolling reduction in the finish rolling is hot-rolled at a temperature lower than the Ar3 transformation point; winding the hot-rolled steel sheet at a winding temperature of 640 to 750° C.; pickling the coiled steel sheet; cold rolling the pickled steel sheet at a rolling reduction rate of 88 to 96%; and annealing the cold-rolled steel sheet in a temperature range of higher than 400° C. to a temperature that is 20° C. lower than the recrystallization temperature.