Abstract: A method of producing a grain-oriented electrical steel sheet with a very low core loss comprises the steps of obtaining a rolled strip of final product thickness using as a starting material molten steel consisting of not more than 0.10 wt % C, 2.5-7.0 wt % Si, ordinary inhibitor components and the balance of iron and unavoidable impurities, heating the strip to a temperature range of not less than 700.degree. C. at a heating rate of not less than 80.degree. C./s and within 0.1 second after the maximum temperature has been reached cooling the strip at a cooling rate of not less than 50.degree. C./s, and subjecting the strip to decarburization annealing and final finish annealing.