Abstract In this paper, we study the following fractional Choquard equation with critical or supercritical growth $$\begin{aligned} \ (-\Delta )^su+V(x)u=f(x,u)+\lambda \left[ |x|^{-\mu }*|u|^p\right] p|u|^{p-2}u, \quad x \in {\mathbb {R}}^N, \end{aligned}$$ (<...