We investigate the following nonlinear system

$$\{\begin{array}{l}-(a+b{\int }_{\mathrm{\Omega }}|\mathrm{\nabla }u{|}^{2}dx)\mathrm{\Delta }u+\varphi u=\lambda u+\mu |u{|}^{2}u,x\in \mathrm{\Omega },\\ -\mathrm{\Delta }\varphi =u^2,x\in \mathrm{\Omega },\\ u=\varphi =0,x\in \mathrm{\partial }\mathrm{\Omega },\end{array}$$

with $a,b>0$, $\lambda ,\mu \in \mathbb{R}$, and $\mathrm{\Omega }\subset {\mathbb{R}}^3$ is bounded with smooth boundary. Let ${\lambda }_1>0$ be the first eigenvalue of $(-\mathrm{\Delta }u,H_0^1(\mathrm{\Omega }))$. We get that for certain $\tilde{\mu }>0$ there exists at least one least energy sign-changing solution for the above system if $\lambda <a{\lambda }_1$ and $\mu >\tilde{\mu }$. In addition, we remark that the nonlinearity $\lambda u+\mu |u{|}^{2}u$ does not satisfy the growth conditions.