A quench solidification method, wherein a steel cast strip having a mean grain size 50 .mu.m or more is prepared and then the steel cast strip is rolled to produce a non-oriented electrical steel sheet having high magnetic flux density in both L and C directions. However the magnetic flux density reduces when the cold reduction rate exceeds 70%. To avoid this problem the non-oriented electrical steel sheet is manufactured with a ratio of at least 4 of the integrated intensity of the {100} plane for a given sample of steel to the integrated intensity of {100} plane for a "random" sample in which crystal grains have random orientations; and a cold reduction rate of the cold-rolling is between 70% and 85%. The superheating degree of the molten steel can be 70.degree. C. or more.