This paper considers the existence and multiplicity of normalized solutions for the following Schrödinger–Poisson equation involving p-Laplacian operator and Hardy term \(\begin{aligned} {\left\{ \begin{array}{ll}-\Delta _p u-\frac{\mu }{|x|^p}|u|^{p-2} u+\kappa \phi |u|^{p-2} u=\lambda |u|^{p-2} u+|u|^{q-2} u, & \text { in } \mathbb {R}^3,\\ -\Delta \phi =|u|^p, & \text { in } \mathbb {R}^3,\\ \int _{\mathbb {R}^3}|u|^p =c>0, \end{array}\right. } \end{aligned}\) where \(1<p<3\) , \(p+\frac{p^{2}}{3}<q<p^{*}:=\frac{3p}{3-p}\) , \(0\le \mu <\bar{\mu }:=\left( \frac{3-p}{p}\right) ^p\) , \(\lambda \) is a Lagrange multiplier and \(\kappa >0\) is a parameter. We prove the existence of normalized solution by using the Pohozaev manifold and obtain the infinitely many radial solutions by a fountain theorem type argument. Moreover, we explore the asymptotic behavior of normalized solutions as \(\mu \rightarrow 0\) and \(\kappa \rightarrow 0\) .
