A method of producing a grain-oriented electrical steel sheet with a very low core loss comprising the steps of obtaining a rolled strip of intermediate product thickness using as a starting material molten steel consisting essentially of not more than 0.10 wt % C, 2.5-7.0 wt % Si, 0.02-0.15 wt % Mn, 0.001-0.050 wt % S, 0.010-0.040 wt % soluble Al, 0.0030-0.0200 wt % N, with a member selected from the group consisting of AlN, MnS and a mixture thereof as an inhibitor component and the balance iron and unavoidable impurities;
- subjecting the strip to hot rolling and a single cold rolling to obtain a rolled strip of final product thickness in which the single cold rolling results in obtaining a high flux density in the steel sheet;
- decarburization annealing the strip by a decarburization annealing process that includes a heating phase wherein the rolled strip of final product thickness in the heating phase of the decarburization annealing is rapidly heated to a temperature range of not less than 700.degree. C. at a heating rate of not less than 80.degree. C./s by passing electric current through the rolled strip at an entry side of a heater;
- cooling the heated strip at an exit side of the heater to a temperature range of 600.degree.-840.degree. C. at a cooling rate of not less than 50.degree. C./s within 0.1 second after the temperature range of not less than 700.degree. C. has been reached, the rapid heating and cooling being incorporated into the heating phase of the decarburization annealing and carried out in a non-oxidizing atmosphere to suppress formation of fayalite and to obtain forsterite during final finish annealing, whereby primary recrystallization grains are obtained having a precipitate size on the order of 100 .ANG.;
- and subjecting the strip to final finish annealing and decarburization annealing to obtain fine secondary recrystallization grains in which the primary recrystallization grain texture is maintained.