  In this work, we consider the reconstruction scenario of new agegraphic dark
energy (NADE) model and $f(G)$ theory of gravity with $G$ representing the
Gauss-Bonnet invariant in the flat FRW spacetime. In this context, we assume a
solution of the scale factor in power-law form and study the correspondence
scenario. A new agegraphic $f(G)$ model is constructed and discussed
graphically for the evolution of the universe. Using this model, we investigate
the different eras of the expanding universe and stability with the help of the
equation of state (EoS) parameter $\omega_{eff}$ and squared speed of sound
$v_s^2$, respectively. It is mentioned here that the reconstructed model
represents the quintessence era of the accelerated expansion of the universe
with instability. Moreover, the statefinder trajectories are studied and we
find out that the model is not capable of reaching the $\Lambda$CDM phase of
the universe.
