  In this paper, we reconstruct the holographic dark energy in the framework of
$f(G)$ modified theory of gravity, where $G$ is Gauss-Bonnet invariant. In this
context, we choose the infrared cut-off as Granda-Oliveros cut-off which is
proportional to the Hubble parameter $H$ and its first derivative with respect
to the cosmic time $t$. We reconstruct $f(G)$ model with the inclusion of HDE
and three well-known forms of the scale factor $a(t)$, i.e. the emergent, the
logamediate and the intermediate scale factors. The reconstructed model as well
as equation of state parameter are discussed numerically with the help of
graphical representation to explore the accelerated expansion of the universe.
Moreover, the stability of the models incorporating all the scale factors is
checked through squared speed of sound $v_s^2$.
