This paper deals with the generalized Choquard equation with an attractive inverse power potential. Using variational method, we prove the existence of the least action ground state \(\phi _{\omega }\) for the corresponding stationary equation and further prove that if \(\partial _{\lambda }^{2}{\mathcal {A}}_{\omega }(\phi _{\omega }^{\lambda })\big |_{\lambda =1}\le 0\) , then the corresponding standing wave \(e^{i \omega t}\phi _{\omega }(x)\) is strongly unstable. Here \(\omega \in {\mathbb {R}}\) is a frequency, \({\mathcal {A}}_{\omega }\) is the action functional and \(\phi _{\omega }^{\lambda }(x):=\lambda ^{\frac{d}{2}}\phi _{\omega }(\lambda x)\) is \(L^{2}\) -invariant scaling.
