  We study finite-time future singularities in $\mathcal{F}(R,G)$-gravity,
where $R$ and $G$ are the Ricci scalar and the Gauss-Bonnet invariant,
respectively. In particular, we reconstruct the $F(G)$-gravity and
$\mathcal{F}(R,G)$-gravity models realizing the finite-time future
singularities. We discuss a possible way to cure the finite-time future
singularities in $\mathcal{F}(R,G)$-gravity by taking into account higher-order
curvature corrections or effects of viscous fluids.
