  In this paper, we investigate the new agegraphic dark energy model in the
framework of Brans-Dicke theory which is a natural extension of the Einstein's
general relativity. In this framework the form of the new agegraphic dark
energy density takes as $\rho_{q} =3n^2 \Phi(t)\eta^{-2}$, where $\eta$ is the
conformal age of the universe and $\Phi(t)$ is the Brans-Dicke scalar field
representing the inverse of the time-variable Newton's constant. We derive the
equation of state of the new agegraphic dark energy and the deceleration
parameter of the universe in the Brans-Dicke theory. It is very interesting to
find that in the Brans-Dicke theory the agegraphic dark energy realizes
quintom-like behavior, i.e., its equation of state crosses the phantom divide
$w=-1$ during the evolution. We also compare the situation of the agegraphic
dark energy model in the Brans-Dicke theory with that in the Einstein's theory.
In addition, we discuss the new agegraphic dark energy model with interaction
in the framework of the Brans-Dicke theory.
