Consider the nonparametric regression model $Y_{ni};=;g(x_{ni})+{epsilon}_{ni}$ ($1;{leq};i;{leq};n$), where g($cdot$) is an unknown regression function, $x_{ni}$ are known fixed design points, and the correlated errors {${epsilon}_{ni}$, $1;{leq};i;{leq};n$} have the same distribution as {$V_i$, $1;{leq};i;{leq};n$}, here $V_t;=;{sum}^{infty}_{j=-{infty}};{psi}_je_{t-j}$ with ${sum}^{infty}_{j=-{infty}};|{psi}_j|$ < $infty$ and {$e_t$} are negatively associated random variables. Under appropriate conditions, we derive a Berry-Esseen type bound for the estimator of g($cdot$). As corollary, by choice of the weights, the Berry-Esseen type bound can attain O($n^{-1/4}({log};n)^{3/4}$).