  This paper is concerned with the following quasilinear Schr\"{o}dinger system
in the entire space $\mathbb R^{N}$($N\geq3$): $$\left\{\begin{align} &-\Delta
u+A(x)u-\frac{1}{2}\triangle(u^{2})u =
\frac{2\alpha}{\alpha+\beta}|u|^{\alpha-2}u|v|^{\beta},\\ &-\Delta
v+Bv-\frac{1}{2}\triangle(v^{2})v=\frac{2\beta}{\alpha+\beta}|u|^{\alpha}|v|^{\beta-2}v.\end{align}\right.
$$ By establishing a suitable constraint set and studying related minimization
problem, we prove the existence of ground state solution for $\alpha,\beta>1$,
$2<\alpha+\beta<\frac{4N}{N-2}$. Our results can be looked on as a
generalization to results by Guo and Tang (Ground state solutions for
quasilinear Schr\"{o}dinger systems, J. Math. Anal. Appl. 389 (2012) 322).
