  In this work, a cosmological model inspired by string theory with
Gauss-Bonnet term coupled to the fermionic field is taken into consideration.
The self-interaction potential is considered as a combination of the scalar and
pseudo-scalar invariants. Here the cosmological contribution of the coupling of
Gauss-Bonnet term with a non-Dirac fermionic field--characterized by an
\textit{interaction term}$L_{DG} ^2$-- is investigated. It is observed that the
new type of coupling plays a significant role in the accelerating behavior of
the universe. Specifically, in addition to the late time acceleration for the
universe, $L_{DG} ^2$ produces an early decelerating behavior. The behavior of
the equation-of-state parameter $(w)$ is such that it guarantees the stability
of the theory.
