To obtain a grain oriented silicon steel sheet with low iron loss, used for an iron core for a transformer, etc.

A silicon steel slab, having a composition containing, by weight ratio, 0.0030-0.090% C, 2.0-4.5% Si, 0.05-0.15% Mn, 0.01-0.04%, in total, of one or both of S and Se, 0.1-3.0% Al, and ≤0.0100% N, is used as a stock. After the slab is hot-rolled, the resultant steel plate is cold-rolled at 10 to 50% draft R(%) or warm-rolled at ≤400°C. Subsequently, annealing is applied under the condition that the temp. rise rate H (°C/s) between 400 and 800°C satisfies 8≤H(°C/s) ≤36-0.48R (%). Then, cold rolling is carried out two or more times while performing process annealing between cold rolling stages, and the resultant steel sheet is subjected to decarburizing annealing and then to final finish annealing.