  In this paper, we study the discrete Kirchhoff-Choquard equation $$
-\left(a+b \int_{\mathbb{Z}^3}|\nabla u|^{2} d \mu\right) \Delta u+V(x)
u=\left(R_{\alpha} *F(u)\right)f(u),\quad x\in \mathbb{Z}^3, $$ where $a,\,b>0$
are constants, $R_{\alpha}$ is the Green's function of the discrete fractional
Laplacian with $\alpha \in(0,3)$, which has no singularity but has same
asymptotics as the Riesz potential. Under some suitable assumptions on $V$ and
$f$, we prove the existence of nontrivial solutions and ground state solutions
by variational methods.
