  We are concerned with the following Schr\"odinger-Poisson equation with
critical nonlinearity: \[\left\{\begin{gathered}
  - {\varepsilon ^2}\Delta u + V(x)u + \psi u = \lambda |u{|^{p - 2}}u +
|u{|^4}u{\text{in}}{\mathbb{R}^3}, \hfill
  - {\varepsilon ^2}\Delta \psi = {u^2}{\text{in}}{\mathbb{R}^3},{\text{}}u >
0,{\text{}}u \in {H^1}({\mathbb{R}^3}), \hfill \end{gathered} \right. \] where
$\varepsilon > 0$ is a small positive parameter, $\lambda > 0$, $3 < p \le 4$.
Under certain assumptions on the potential $V$, we construct a family of
positive solutions ${u_\varepsilon} \in {H^1}({\mathbb{R}^3})$ which
concentrates around a local minimum of $V$ as $\varepsilon \to 0$.
