The purpose of this paper is to study the following singularly perturbed N-Laplacian Kirchhoff-type equation: \(\begin{aligned} \left\{ \begin{aligned}&-\left( \varepsilon ^{N}+\varepsilon ^{N} b\int _{ \mathbb {R}^{N}}|\nabla v|^{N} \textrm{d}x \right) \Delta _{N} v+V(x)|v|^{N-2}v=Q(x)f(v),&x\in \mathbb {R}^{N},\\&v\in W^{1,N}(\mathbb {R}^{N}), \end{aligned} \right. \end{aligned}\) where \(N\ge 2\) , b is a positive constant, \(\Delta _{N}\) is the N-Laplacian operator, \(\varepsilon \) is a positive parameter, \(V,Q\in {\mathcal {C}}\left( \mathbb {R}^N, \mathbb {R}\right) \) and f has critical exponential growth at infinity. In order to overcome difficulties due to lack of compactness aroused by the critical exponential growth of f and quasilinear characteristic of the equation, we develop some delicate analyses to give a fine threshold of the Mountain-Pass minimax level and show the existence and concentration of semiclassical ground state solutions for the above equation. In particular, if V remains constant, the concentration occurs at the maximum point set of Q.
