  In this paper we show that power-law inflation can be realized in non-minimal
gravitational coupling of Yang-Mills field with a general function of the
Gauss-Bonnet invariant in the framework of Einstein gravity. Such a non-minimal
coupling may appear due to quantum corrections. We also discuss the non-minimal
Yang-Mills-$f(G)$ gravity in the framework of modified Gauss-Bonnet action
which is widely studied recently. It is shown that both inflation and late-time
cosmic acceleration are possible in such a theory.
