The present invention is a method of using a continuous casting-continuous hot rolling facility to cast a medium thickness bar, making the bar reach a final hot rolling inlet while a temperature over 1200° C. for holding the solid-solute state of AlN is maintained, hot rolling the bar, and rapidly cooling it to make fine AlN precipitate and thereby efficiently an inexpensively produce high flux density grain-oriented silicon steel sheet without any high temperature heating of the bar.