  The present study is concerned with the following Schr\"{o}dinger-Poisson
system involving critical nonlocal term with general nonlinearity: $$ \left\{
\begin{array}{ll} -\Delta u+V(x)u- \phi |u|^3u= f(u), & x\in\mathbb{R}^3,
-\Delta \phi= |u|^5, & x\in\mathbb{R}^3,\\ \end{array} \right. $$ Under certain
assumptions on non-constant $V(x)$, the existence of a positive least energy
solution is obtained by using some new analytical skills and Poho\v{z}aev type
manifold. In particular, the Ambrosetti-Rabinowitz type condition or
monotonicity assumption on the nonlinearity is not necessary.
