  In this paper, we consider the quasilinear Schr\"{o}dinger system in $\mathbb
R^{N}$($N\geq3$): $$\left\{\begin{align} &-\Delta u+
A(x)u-\frac{1}{2}\triangle(u^{2})u=\frac{2\alpha
}{\alpha+\beta}|u|^{\alpha-2}u|v|^{\beta},\\ &-\Delta v+
Bv-\frac{1}{2}\triangle(v^{2})v=\frac{2\beta
}{\alpha+\beta}|u|^{\alpha}|v|^{\beta-2}v,\end{align}\right. $$ where
$\alpha,\beta>1$, $2<\alpha+\beta<\frac{4N}{N-2}$,$B>0$ is a constant. By using
a constrained minimization on Nehari-Poho\v{z}aev set, for any given integer
$s\geq2$, we construct a non-radially symmetrical nodal solution with its $2s$
nodal domains.
