  In this paper, we study a class of fractional Schr\"{o}dinger equation
\begin{equation} \label{eq0} \left\{ \begin{aligned} &(-\Delta)^{s}u=\lambda
u+a(x)|u|^{p-2}u,\\ &\int_{\mathbb{R}^{N}}|u|^{2}dx=c^{2},\ u\in
H^{s}(\mathbb{R}^{N}), \end{aligned} \right. \end{equation} where $N>2s$,
$s\in(0,1)$ and $p\in(2,2+4s/N), c>0$. $a(x)\in C(\mathbb{R}^{N},\mathbb{R})$
is a positive potential function. By using Fixed Point Theorem of Brouwer,
barycenter function and variational method, we obtain the existence of
normalized bound solutions for the problem.
