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In this paper, we consider the following Schrödinger–Poisson system with strong singularity $$\begin{cases} -\Delta{u}+\phi u=f(x)u^{-\gamma}, & x\in \Omega,\\ -\Delta{\phi}=u^2, & x\in\Omega,\\ u>0, & x\in\Omega,\\ u=\phi=0, & x\in\partial\Omega, \end{cases}$$ where $\Omega\subset \mathbb{R}^3$ is a smooth bounded domain, $\gamma>1$, $f\in L^1(\Omega)$ is a positive function (i.e. $f(x)>0$ a.e. in $\Omega$). A necessary and sufficient condition on the existence and uniqueness of positive weak solution of the system is obtained. The results supplement the main conclusions in recent literature.