Abstract: A method of producing a grain-oriented magnetic steel sheet exhibiting a very low core loss and high magnetic flux density uses a slab of silicon steel containing Al, B, N, and S and/or Se. The method employs hot rolling conducted such that the rolling reduction falls within the range of from about 85 to 99%, and the hot-rolling finish temperature falls within the range of from 950.degree. to 1150.degree. C. and is based on the contents of Si, Al and B. The hot-rolled steel sheet is rapidly cooled at a cooling rate of about 20.degree. C./s and is coiled at a temperature of about 670.degree. C. or lower. Hot-rolled sheet annealing or intermediate annealing is executed by heating the hot-rolled steel sheet up to about 800.degree. C. at a heating rate of from 5.degree. to 25.degree. C./s and holding at a temperature of from about 800.degree. to 1125.degree. C. for a period not longer than about 150 seconds.