In this paper we discuss the following Kirchhoff equation
\left\{
\begin{array}{lr}
-\left(a+b \int_{\mathbb{R}^3}|\nabla u|^{2} d x\right) \Delta u+V(x)u+\lambda u=\mu|u|^{q-2}u+|u|^{p-2}u \ {\rm in}\ \mathbb{R}^3,&\\
\int_{\mathbb{R}^{3}}u^{2}dx=c^2,
\end{array}
\right.
where a, b, µ and c are positive numbers, λ is unknown and appears as a Lagrange multiplier,
14/3<q<p<6 and V is a continuous non-positive function vanishing at infinity.
Under some mild assumptions on V , we prove the existence of a mountain pass normalized solution. To the author’s knowledge, it is the first time to study the existence of
normalized solution to Kirchhoff equation with potential via the minimax principle.
