Further improving the magnetic properties of oriented electrical steel sheet than before. By mass% C: 0.002% to 0.080% or less, Si: 2.00% to 8.00% or less, Mn: 0.02% to 0.50% or less, the acid-soluble Al less 0.003% 0.010% or more, the S and / or Se in a total 0.005% or more than 0.010% and Sn and / or Sb contained 1.000% 0.005% to a total suppressing N to less than 0.006% or the balance being a steel slab having the component composition of Fe and unavoidable impurities 1300 ℃ heating below, and hot-rolled steel sheet is subjected to hot rolling steel slab, to the heat-rolled steel sheet, cold with a final thickness is subjected to two or more cold rolling sandwiching once or intermediate annealing and rolled steel sheet was subjected to primary recrystallization annealing to the cold-rolled steel sheet, the grain-oriented electrical steel sheet subjected to the annealing separator applied to the surface secondary recrystallization annealing from the cold-rolled steel sheet after the primary recrystallization annealing to provide a process for the production.