In this paper, we consider the normalized solutions for the following nonlinear Schrödinger-Choquard system \(\begin{aligned} {\left\{ \begin{array}{ll} -\Delta u+(V_1(x)+\lambda _1)u=\mu _1\int _{\mathbb {R}^3}\frac{|u(y)|^p}{|x-y|}dy|u|^{p-2}u+\beta uv,& ~\textrm{in}~\mathbb {R}^3,\\ -\Delta v+(V_2(x)+\lambda _2)v=\mu _2\int _{\mathbb {R}^3}\frac{|v(y)|^q}{|x-y|}dy|v|^{q-2}v+\frac{\beta }{2} u^2,& ~\textrm{in}~\mathbb {R}^3,\\ \int _{\mathbb {R}^3}|u|^2dx=a,~~~~~~~\int _{\mathbb {R}^3}|v|^2dx=b, \end{array}\right. } \end{aligned}\) where the exponents \(\frac{5}{3}<p,q<\frac{7}{3}\) are \(L^2\) -subcritical, \(\mu _1,\mu _2,a,b>0, \beta \in \mathbb {R}\setminus \{0\}\) , \(V_1,V_2:\mathbb {R}^3\rightarrow \mathbb {R}\) are trapping potentials. Based on the variational methods and rearrangement inequalities, we prove the existence of normalized solutions under the trivial potentials and non-trivial potentials.
