Abstract: This invention is to save the energy by heating a slab at high temperature for producing non-oriented electrical steel sheets having excellent magnetic properties uniform over the full length thereof, without carrying out a long soaking, for which a continuously cast slab having a specified chemical composition is heated at a high temperature, and a heat cycle is then defined such that the slab is passed twice nearly around precipitation noses, thereby to coarse the AIN precipitates over the full length of the slab, and the slab is annealed under a specified condition after the hot rolling so that AlN is coarsened and the ferrite grains recrystallize and grow.