We study all four types of finite-time future singularities emerging in late-time accelerating (effective quintessence/phantom) era from F(R,G)-gravity, where R and G are the Ricci scalar and the Gauss-Bonnet invariant, respectively. As an explicit example of F(R,G)-gravity, we also investigate modified Gauss-Bonnet gravity, so-called F (G)-gravity. In particular, we reconstruct the F (G)-gravi...