  We are concerned with the following Schr\"odinger-Newton problem
  \begin{equation}
  -\varepsilon^2\Delta u+V(x)u=\frac{1}{8\pi \varepsilon^2}
  \big(\int_{\mathbb R^3}\frac{u^2(\xi)}{|x-\xi|}d\xi\big)u,~x\in \mathbb R^3.
\end{equation} For $\varepsilon$ small enough, we show the uniqueness of
positive solutions concentrating at the nondegenerate critical points of
$V(x)$. The main tools are a local Pohozaev type of identity, blow-up analysis
and the maximum principle. Our results also show that the asymptotic behavior
of concentrated points to Schr\"odinger-Newton problem is quite different from
those of Schr\"odinger equations.
