In this paper we study the existence of normalized solutions for the following nonautonomous Schrödinger-Poisson system with critical growth \(\begin{aligned} {\left\{ \begin{array}{ll} -\Delta u-\phi |u|^3u=\lambda u+Q(x)|u|^{q-2}u+|u|^4u, & x \in {\mathbb {R}}^{3},\\ -\Delta \phi =|u|^5, & x \in {\mathbb {R}}^{3}, \end{array}\right. } \end{aligned}\) having prescribed mass \(\begin{aligned} \int _{{\mathbb {R}}^3}|u|^2dx=m, \end{aligned}\) where \(u\in H^1({\mathbb {R}}^3), m>0, 2<q<6 \) , Q is a non-const potential function, and \(\lambda \in {\mathbb {R}}\) appears as a Lagrange multiplier. In the \(L^2\) -subcritical regime: \(2< q <\frac{10}{3}\) , by imposing some new conditions on potential Q, we show that the corresponding Pohozaev manifold is a natural constraint and obtain the existence of normalized ground state solutions; while in the \(L^2\) -critical and \(L^2\) -supercritical regime: \(\frac{10}{3} \le q < 6\) , by using the classical deformation lemma we show the existence of normalized ground states on the Pohozaev manifold of the associated energy functional, under some further assumptions proposed on Q.
