Abstract: Let （X,Y）, （X₁, Y₁）,（X₂, Y₂）,… be a sequenoe of i. i. d. R^dxR~1-valued random variables with E|Y|＜∞. This paper studies the asymptotic normality for nearest neighbor estimator of nonparametric regression function, i.e. under certain conditions \fracm_n(x)-m(x)\left(\sum_i=1^k \nu_n^2 \delta(x)\right)^1 / 2 \xrightarrow\mathscrL N(0,1).