  In this paper, we study the existence and asymptotic properties of solutions
to the following fractional Kirchhoff equation \begin{equation*}
\left(a+b\int_{\mathbb{R}^{3}}|(-\Delta)^{\frac{s}{2}}u|^{2}dx\right)(-\Delta)^{s}u=\lambda
u+\mu|u|^{q-2}u+|u|^{p-2}u \quad \hbox{in $\mathbb{R}^3$,} \end{equation*} with
a prescribed mass \begin{equation*} \int_{\mathbb{R}^{3}}|u|^{2}dx=c^{2},
\end{equation*} where $s\in(0, 1)$, $a, b, c>0$,
$2<q<p<2_{s}^{\ast}=\frac{6}{3-2s}$, $\mu>0$ and $\lambda\in\mathbb{R}$ as a
Lagrange multiplier. Under different assumptions on $q<p$, $c>0$ and $\mu>0$,
we prove some existence results about the normalized solutions. Our results
extend the results of Luo and Zhang (Calc. Var. Partial Differential Equations
59, 1-35, 2020) to the fractional Kirchhoff equations. Moreover, we give some
results about the behavior of the normalized solutions obtained above as
$\mu\rightarrow0^{+}$.
