  In this paper we implement the new agegraphic dark energy model with
quintessence field. We demonstrate that the new agegraphic evolution of the
universe can be described completely by a single quintessence field. Its
potential as a function of the quintessence field is reconstructed numerically.
In particular, the analytical solution of the new agegraphic quintessence dark
energy model (NAQDE) is approximately obtained in the matter-dominated epoch.
Furthermore, we investigate the evolution of the NAQDE model in the
$\omega-\omega'$ phase plane. It turns out that by quantum corrections, the
trajectory of this model lies outside the thawing and freezing regions at early
times. But at late times, it enters the freezing regions and gradually
approaches to a static cosmological constant state in the future. Therefore the
NAQDE should belong to the freezing model at late times. For comparison, we
further extend this model by including the interaction between the NADE and DM
and discuss its evolution in the $\omega-\omega'$ phase plane.
