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In this paper, we consider the quasilinear Schr\"{o}dinger system in $\mathbbR^{N}$($N\geq3$): $$\left\{\begin{align} &-\Delta u+A(x)u-\frac{1}{2}\triangle(u^{2})u=\frac{2\alpha}{\alpha+\beta}|u|^{\alpha-2}u|v|^{\beta},\\ &-\Delta v+Bv-\frac{1}{2}\triangle(v^{2})v=\frac{2\beta}{\alpha+\beta}|u|^{\alpha}|v|^{\beta-2}v,\end{align}\right. $$ where$\alpha,\beta>1$, $2<\alpha+\beta<\frac{4N}{N-2}$,$B>0$ is a constant. By usinga 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.

Multiple nonsymmetric nodal solutions for quasilinear Schr\"{o}dinger system