  In this paper, we use variational methods to prove the existence of positive
solution for the following class of elliptic equation $$
-\epsilon^{2}\Delta{u}+V(z)u=f(u) \,\,\, \mbox{in} \,\,\, \mathbb{R}^{2}, $$
where $\epsilon >0$ is a positive parameter, $V$ is a saddle-like potential and
$f$ has an exponential critical growth.
