In this paper, we study the following coupled fractional Choquard system $$\left\{\aligned&(-\Delta)^s u+V(x)u=\frac{2q}{p+q}\bigl(I_\alpha\ast|u|^p\bigr)|v|^{q-2}v,\\ &(-\Delta)^s v+V(x)v=\frac{2p}{p+q}\bigl(I_\alpha\ast|v|^q\bigr)|u|^{p-2}u,\\ &\ u(x)\to0\ \ \hbox{and}\ \ v(x)\to0\ \ \hbox{as}\ |x|\to\infty,\endaligned\right. $$ where $02s,\frac{N+\alpha}{N}