In a method of producing a grain-oriented electrical steel sheet by subjecting a coil for grain-oriented electrical steel sheet after cold rolling to a primary recrystallization annealing, applying an annealing separator thereon, and conducting final annealing, rapid heating is conducted at a rate of not less than 80° C./sec from 500° C. to 700° C. in the course of heating for the primary recrystallization annealing, and a temperature keeping treatment is conducted for 2 to 100 hours from 700° C. to 1000° C. in the course of heating for the final annealing, and further, the final annealing is preferably conducted by laying a thermal insulation material on an upper surface of a coil supporting stand in an annealing furnace used for the final annealing concentrically from the outer periphery of the coil supporting stand and over an area of not less than 20% of the radius of the coil supporting stand.