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In this paper, we use variational methods to prove the existence of positivesolution 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.

Existence of positive solution for a nonlinear elliptic equation with  saddle-like potential and nonlinearity with exponential critical growth in  $\mathbb{R}^{2}$