This article concerns the existence of multi-bump positive solutions for a class of fractional Schrödinger-Poisson system involving logarithmic nonlinearity \(\begin{aligned} \left\{ \begin{array}{ll} \left( -\Delta \right) ^{s} u+\lambda V(x)u-\phi u= u \log {u^{2}}& \quad \text { in }\mathbb {R}^{3}, \\ \left( -\Delta \right) ^{t}\phi =u^{2}& \quad \text { in }\mathbb {R}^{3}, \\ \end{array} \right. \end{aligned}\) where \(s,t\in (0,1)\) , \(4s+2t\ge 3\) and the nonnegative continuous function V has the deepening potential well \(int V^{-1}(0)\) consisting of k disjoint components \(\Omega _{1},\Omega _{2}, \cdots ,\Omega _{k}\) . By applying suitable variational arguments, we analyze that the system has at least \(2^{k}-1\) multi-bump positive solutions as the parameter \(\lambda >0\) is large enough.
