In this paper, we consider the qualitative analysis of solutions for the following Kirchhoff equation with Hardy nonlinearities: \( \left \{\begin{aligned} &-(a+b\int _{\mathbb{R}^{N}}|\nabla u|^{2} dx)\Delta u=\lambda u+\frac{|u|^{p - 2}u}{|x|^{\beta}}+\mu \frac{|u|^{q - 2}u}{|x|^{\beta}}, &&\text{ in } \mathbb{R}^{N},\\ &\int _{\mathbb{R}^{N}} u^{2} dx = c^{2}, \end{aligned}\right . \) where $N\geq 3,~0<\beta <2,~2<q<p<2^{*}_{\beta}:=\frac{2(N-\beta )}{N-2}$, $a,b,c>0,~\mu >0$ and $\lambda \in \mathbb{R}$ appears as a Lagrange multiplier. By developing a perturbed Pohozaev constraint approach, we show the existence of normalized solutions under the mixed $L^{2}$-critical case where $2< q<\frac{2(N+4-\beta )}{N}<p<2^{*}_{\beta}$ and ground state solutions in the $L^{2}$-supercritical case where $\frac{2(N+4-\beta )}{N}< q< p<2^{*}_{\beta}$, respectively. Moreover, the asymptotic behaviors of the normalized solutions are also obtained.
