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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 futuresingularities. We discuss a possible way to cure the finite-time futuresingularities in $\mathcal{F}(R,G)$-gravity by taking into account higher-ordercurvature corrections or effects of viscous fluids.

Finite-time singularities in modified $\mathcal{F}(R,G)$-gravity and singularity avoidance