  In this paper, we study the following Kirchhoff type problem:% $$
\left\{\aligned&-\bigg(\alpha\int_{\bbr^3}|\nabla u|^2dx+1\bigg)\Delta
u+(\lambda a(x)+a_0)u=|u|^{p-2}u&\text{ in }\bbr^3,\\%
&u\in\h,\endaligned\right.\eqno{(\mathcal{P}_{\alpha,\lambda})}% $$ where
$4<p<6$, $\alpha$ and $\lambda$ are two positive parameters, $a_0\in\bbr$ is a
(possibly negative) constant and $a(x)\geq0$ is the potential well. By the
variational method, we investigate the existence of nontrivial solutions to
$(\mathcal{P}_{\alpha,\lambda})$. To our best knowledge, it is the first time
that the nontrivial solution of the Kirchhoff type problem is found in the
indefinite case. We also obtain the concentration behaviors of the solutions as
$\lambda\to+\infty$.
