A non-oriented electrical steel sheet is obtained by subjecting a slab containing C: not more than 0.005 mass %, Si: 1.0-5.0 mass %, Mn: 0.04-3.0 mass %, sol. Al: not more than 0.005 mass %, P: 0.03-0.2 mass %, S: not more than 0.005 mass %, N: not more than 0.005 mass %, B: not more than 0.001 mass %, and Se: not more than 0.001 mass % and satisfying sol. Al+C+5B+5Se≦0.005 mass % to hot rolling, cold rolling and finish annealing. A sheet temperature at the outlet side of the rolling machine in at least one pass of the final cold rolling is set to a range of 100-300° C. to provide S/2M of not less than 1.0 and S/5C of not less than 1.0 when X-ray intensity ratios of {001} , {111} and {001} in a central layer in a thickness direction are S, M and C, respectively.