A grain oriented electrical steel sheet comprises metal part containing Si: about 2.5 to about 5.0 mass % and Cr: about 0.05 to about 1.0 mass %, and an insulation coating formed on a surface of the metal part. A tension imparted to the metal part in the rolling direction by the insulation coating is not smaller than about 3.0 MPa. Magnetic flux density B.sub.8 satisfies a specific relation formula. A plurality of linear strains or grooves are formed in a surface of the steel sheet and linearly extended at an angle of not larger than about 45.degree. (in each direction) relative to a direction perpendicular to a rolling direction such that an interval D of the linear strains or grooves satisfies a specific relation formula depending on the Cr content. A grain oriented electrical steel sheet is thereby obtained which has lower iron loss after domain refining treatment than conventional values. In the production process for the steel sheet of the invention, parameters such as annealing temperature in annealing before final cold rolling are controlled.