This article is devoted to study the following quasilinear Schrödinger system with super-quadratic condition:

$$\{\begin{array}{c}-\mathrm{\Delta }u+V_1(x)u-\mathrm{\Delta }(u^2)u=h(u,v),x\in {\mathbb{R}}^N,\\ -\mathrm{\Delta }v+V_2(x)v-\mathrm{\Delta }(v^2)v=g(u,v),x\in {\mathbb{R}}^N,\end{array}$$

where $N\ge 3$, $V_1(x)$, $V_2(x)$ are variable potentials and $h$, $g$ satisfy some conditions. By establishing a suitable Nehari-Pohožaev type constraint set and considering related minimization problem, we prove the existence of ground states.