In the present paper, we are concerned with the existence of positive normalized solutions with prescribed \(L^{2}\) -norm \(\Vert u\Vert _{2}=m\) for the following Choquard equations involving a potential \(\begin{aligned} {\left\{ \begin{array}{ll} -\Delta u+V(x)u+\lambda u=(I_{\alpha }*F(u))f(u) & {\textrm{in}}\quad \mathbb {R}^{N},\\ \Vert u\Vert _{2}=m>0, \end{array}\right. } \end{aligned}\) where \(N>2\) , \(I_{\alpha }\) is the Riesz potential of order \(\alpha \in (0,N)\) . Under assumptions on \(L^2\) -supercritical nonlinearity \(F'=f\) , and \(V:\mathbb {R}^{N}\rightarrow \mathbb {R}\) , \(V\leqslant 0\) , and vanishing at infinity, we show the existence of a positive solution \((u,\lambda )\in H^{1}(\mathbb {R}^{N})\times \mathbb {R}^{+}\) by using a min–max principle.
