Abstract: We study the following nonlinear fractional Schrödinger-Poisson system with critical growth: \begin{equation}\label{eqS0.1} \renewcommand{\arraystretch}{1.25} \begin{array}{ll} \left \{ \begin{array}{ll} (-\Delta )^s u+u+\phi u=f(u)+|u|^{2^*_s-2}u,\quad &x\in \mathbb{R}^3, \\ (-\Delta )^t \phi=u^2,& x\in \mathbb{R}^3, \\ \end{array} \right . \end{array} \end{equation} where $0 < s,t < 1$, $2s+2t > 3$ and $2^*_s=\frac{6}{3-2s}$ is the critical Sobolev exponent in $\mathbb{R}^3$. Under some more general assumptions on $f$, we prove that (0.1) admits a nontrivial ground state solution by using a constrained minimization on a Nehari-Pohozaev manifold.

Key words: fractional Schrödinger-Poisson system, Nehari-Pohozaev manifold, ground state solutions, critical growth