  In this paper, we investigated inflationary solutions for a subclass of
Horndeski models where a scalar field is non-minimally coupled with the
Gauss-Bonnet invariant. Examples of canonical scalar field and $k$-essence to
support the early-time acceleration are considered. The formalism to calculate
the perturbations in FRW universe and to derive the spectral index and the
tensor-to-scalar ratio is furnished.
