Reheating a grain-oriented electrical steel sheet slab comprising predetermined components to 1280°C or more and a solid solution temperature of inhibitor substances or more, hot rolling, annealing, and cold rolling it, decarburization annealing it, nitriding it in a strip running state, coating an annealing separator, and finish annealing it during which making a precipitation ratio of N as AlN after hot rolling 20% or less, making a mean grain size of primary recrystallization 7 µm to less than 20 µm, and making a nitrogen increase N in the nitridation within a range of Equation (1) and making nitrogen contents ÃN1 and ÃN2 (front and back, mass%) of a 20% thickness portion of one surface of the steel strip (sheet) within a range of Equation (2): 0.007 - N - 14 / 48 &dlowbar; Ti N solAl &dlowbar; 14 / 27 - N - 14 / 48 &dlowbar; Ti + 0.0025 ÃN ¢ 1 - ÃN ¢ 2 / N 0.35