In this paper, we study the p-Laplacian system with Choquard-type nonlinearity \(\left\{ {\begin{array}{*{20}{l}} \begin{gathered} - {\Delta _p}u + (\lambda a + 1)|u{|^{p - 2}}u = \frac{1}{\gamma }\left( {{R_\alpha }*F(u,v)} \right){F_u}(u,v), \hfill \\ - {\Delta _p}v + (\lambda b + 1)|v{|^{p - 2}}v = \frac{1}{\gamma }\left( {{R_\alpha }*F(u,v)} \right){F_v}(u,v), \hfill \\ \end{gathered} \end{array}} \right.\) on lattice graphs \(\mathbb {Z}^N\) , where \(\alpha \in (0,N),\,p\ge 2,\,\gamma> \frac{(N+\alpha )p}{2N},\,\lambda>0\) is a parameter and \(R_{\alpha }\) is the Green’s function of the discrete fractional Laplacian that behaves as the Riesz potential. Under some assumptions on the functions \(a,\,b\) and F, we prove the existence and asymptotic behavior of ground state solutions by the method of Nehari manifold.
