In a method for producing a grain-oriented electrical steel sheet by subjecting a slab of an inhibitor-less ingredient system containing C: 0.002-0.10 mass%, Si: 2.5-6.0 mass%, Mn: 0.010-0.8 mass% and extremely decreased Al, N, Se and S to hot rolling, hot band annealing, cold rolling, decarburization annealing, application of an annealing separator and finish annealing, when a certain temperature within a range of 700-800°C in a heating process of the decarburization annealing is T1 and a certain temperature as a soaking temperature within a range of 820-900°C is T2, a heating rate R1 between 500°C and T1 is set to not less than 100°C/s and a heating rate R2 between T1 and T2 is set to not more than 15°C/s, whereby a grain-oriented electrical steel sheet having excellent iron loss property and coating peeling resistance is obtained in the inhibitor-less ingredient system while ensuring decarburization property even when rapid heating is performed during the decarburization annealing.