This paper is concerned with the following N-Laplacian Kirchhoff equation with singular term and the nonlinearity \(f(x,\cdot )\) possesses critical exponential growth at infinity, \(\begin{aligned} -\left( 1+b\int _{ \mathbb {R}^{N}}|\nabla u|^{N} \textrm{d}x \right) \Delta _N u+V(x)|u|^{N-2}u=\frac{f(x,u)}{|x|^\eta },\ \ \text{ in } \mathbb {R}^N \text{, } N\ge 2 , \end{aligned}\) where \(b>0\) , \(0<\eta <N\) , \(V\in \mathcal {C}(\mathbb {R}^N,\mathbb {R})\) and \(\Delta _N u:=\textrm{div}(|\nabla u|^{N-2}\nabla u)\) . We develop some delicate analyses to deal with several challenges caused by the complicated interplay among the singular potential \(1/|x|^\eta \) , the nonlocal term \((\int _{\mathbb {R}^N}|\nabla u|^N\textrm{d}x)\Delta _N u\) and the critical exponential growth of the nonlinearity f(x, u). It is worth noting that a key ingredient in restoring the compactness of Cerami sequence is to control the Mountain-pass minimax level by a suitable threshold, this will be done by introducing more natural growth conditions on f and developing some variational techniques. By employing the Mountain-pass theorem, singular Trudinger–Moser inequality and some precise estimates, we establish the existence of ground state solutions for the above problem.
