In a method of producing a grain-oriented electrical steel sheet by hot rolling a steel slab comprising C: 0.001ˆ¼0.10 mass%, Si: 1.0ˆ¼5.0 mass%, Mn: 0.01ˆ¼1.0 mass%, one or two of S and Se: 0.01ˆ¼0.05 mass% in total, sol. Al: 0.003ˆ¼0.050 mass% and N: 0.001ˆ¼0.020 mass%, cold rolling, subjecting to primary recrystallization annealing, applying an annealing separator and finally subjecting to final annealing, the primary recrystallization annealing is conducted so as to control a heating rate S 1 between 500 and 600°C to not less than 100°C/s and a heating rate S2 between 600 and 700°C to not less than 30°C/s but not more than 0.6 x S1, and as a main ingredient of the annealing separator is used MgO having an expected value µ(A) of citric acid activity distribution of 3.5ˆ¼3.8, a cumulative frequency F of 25ˆ¼45% when an activity A is not less than 4.0, whereby a grain-oriented electrical steel sheet having no deterioration of magnetic properties is obtained without causing cracking or chipping due to twining deformation.