To stably improve the magnetic flux density by utilizing induction heating and radiant heating during final annealing of a non-oriented electrical steel sheet. A method of manufacturing a non-oriented electrical steel sheet, including subjecting a slab having a predetermined chemical composition to hot rolling with or without performing hot-rolled sheet annealing, and then to cold rolling either once, or twice or more with intermediate annealing performed therebetween, and then to final annealing, where a material before final cold rolling has a recrystallization ratio of less than 80% and a {100} intensity of 8 or less in a ¼ layer, and in the final annealing, an average heating rate from 600° C. to 720° C. is 50° C./s or higher, and an average heating rate from 720° C. to 760° C. is 5° C./s or higher.