A non-oriented electrical steel sheet is characterized in that the number density of inclusions with an equivalent volume diameter of less than 100 nm contained in the steel sheet is 1.times.10.sup.10 [/mm.sup.3] or less, and that the steel sheet contains, by mass %, C: up to 0.01%, Si: 0.1% to 7.0%. Al: 0.1% to 3.0%. Mn: 0.1% to 2.0%, REM: 0.0003% to 0.05%. Ti: up to 0.02%. S: up to 0.005%. and N: up to 0.005%. the balance Fe and inevitable impurities and the mass % of Al represented by [Al] and the mass % of Ti represented by [Ti] satisfy the equation log([Ti].times.[N])-1.19.times.log([Al].times.[N])+1.84>0 . . . (1).