  In this paper we show that power-law inflation can be realized in non-minimal
gravitational coupling of electromagnetic field with a general function of
Gauss-Bonnet invariant. Such a non-minimal coupling may appear due to quantum
corrections. We also consider modified Maxwell-$F(G)$ gravity in which
non-minimal coupling between electromagnetic field and $f(G)$ occur in the
framework of modified Gauss-Bonnet gravity. It is shown that inflationary
cosmology and late-time accelerated expansion of the universe are possible in
such a theory.
