Summary: We study the existence of positive ground state solutions for the following fractional Kirchhoff type equation \[ \begin{cases} \left(a+b \int_{\mathbb R^3}|(-\Delta)^{\frac{s}{2}}u|^2dx\right) (-\Delta)^su+V(x)u=\mu|u|^{p-2}u+|u|^{2^\ast_s-2}u \;x \in \mathbb R^3 \\ u \in H^S(\mathbb R^3), \end{cases} \] where \(a,b> 0\) are constants, \(\mu\) is a positive parameter, \(2<p<2_S^\ast\) with \(2_S^\ast = \frac{6}{3-2s}\) and \(s\in (0,1)\). Under suitable assumptions on \(V(x)\), by using a monotonicity trick and a global compactness principle, we prove that the equation admits a positive ground state solution if \(s \in (\frac{3}{4},1) \) and \(\mu> 0\) large enough.