In a production of a non-oriented electrical steel sheet by subjecting a slab containing, in mass%, C: not more than 0.0050%, Si: 2.8 to 6.5%, Mn: 0.05 to 2.0%, P: not more than 0.10%, S: not more than 0.0050%, Al: 0.3 to 2.0%, N: not more than 0.0050% and Zn: 0.0005 to 0.0050% to a hot rolling, a hot-band annealing, a cold rolling and a finish annealing, a dew point in the hot-band annealing is set to 0 to 70 °C and an atmosphere of the finish annealing has a nitrogen content of not more than 30 vol% and a dew point of not higher than - 20°C, and a ratio of the amount of nitrogen present as AlN in an entire sheet thickness to the amount of nitrogen present as AlN in a layer from one-side surface of steel sheet to a depth of 1/20 of sheet thickness is made to not less than 5.0, whereby a non-oriented electrical steel sheet having high magnetic flux density and a low iron loss at a high frequency is obtained without decreasing the magnetic flux density and decreasing the productivity.