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The present study is concerned with the following Schr\"{o}dinger-Poissonsystem involving critical nonlocal term $$ \left\{ \begin{array}{ll} -\Deltau+u-K(x)\phi |u|^3u=\lambda f(x)|u|^{q-2}u, & x\in\mathbb{R}^3, -\Delta\phi=K(x)|u|^5, & x\in\mathbb{R}^3,\\ \end{array} \right. $$ where $1<q<2$ and$\lambda>0$ is a parameter. Under suitable assumptions on $K(x)$ and $f(x)$,there exists $\lambda_0=\lambda_0(q,S,f,K)>0$ such that for any$\lambda\in(0,\lambda_0)$, the above Schr\"{o}dinger-Poisson system possessesat least two positive solutions by standard variational method, where apositive least energy solution will also be obtained.

Multiple positive solutions for Schrodinger-Poisson systems involving critical nonlocal term