Let $X_n$ be a standard real symmetric (complex Hermitian) Wigner matrix,$y_1,y_2,\cdots,y_n$ a sequence of independent real random variables independent of $X_n$.Consider the deformed Wigner matrix $H_{n,\alpha}=\frac{X_n}{\sqrt n}+ \frac{1}{n^{\alpha/2}}\mbox{diag}(y_1,\cdots,y_n)$ where $0<\alpha<1$.It is well-known that the average spectral distribution is the classical Wigner semicircle law,i.e.,the Stieltjes transform $m_{n,\alpha}(z)$ converges in probability to the corresponding Stieltjes transform $m(z)$.In this talk we shall give the asymptotic estimate for the expectation $\mathbb{E}m_{n,\alpha}(z)$ and variance $Var(m_{n,\alpha}(z))$,and establish the central limit theorem for linear statistics with sufficiently regular test function.A basic tool in the study is Steins equation and its generalization which naturally leads to a certain recursive equation.