  In this paper, we consider the existence of localized sign-changing solutions
for the $p-$Laplacian nonlinear Schr\"odinger equation $$
-\epsilon^p\Delta_pu+V(x)|u|^{p-2}u=|u|^{p^*-2}u+\mu|u|^{q-2}u,~~u\in
W^{1,p}(\mathbb{R}^N), $$ where $1<p<N$,
$p_N=\max\{p,p^*-1\}<q<p^*=\frac{Np}{N-p}$, $\mu>0$, $\Delta_p$ is the
$p-$Laplacian operator. By using the penalization method together with the
truncation method and a blow-up argument, we establish for small $\epsilon$ the
existence of a sequence of localized nodal solutions concentrating near a given
local minimum point of the potential function.
