  Motivated by the work of Yang et al., \emph{Mod. Phys. Lett. A}, \textbf{26},
191 (2011), we report a study on the New Holographic Dark Energy (NHDE) model
with energy density given by $\rho_D=\frac{3\phi^2}{4\omega}(\mu H^2+\nu
\dot{H})$ in the framework of chameleon Brans-Dicke cosmology. We have studied
a correspondence between the quintessence, the DBI-essence and the tachyon
scalar field models with the NHDE model in the framework of chameleon
Brans-Dicke cosmology. Deriving an expression of the Hubble parameter $H$ and,
accordingly, $\rho_D$ in the context of chameleon Brans-Dicke chameleon
cosmology, we have reconstructed the potentials and dynamics for these scalar
field models. Furthermore, we have examined the stability for the obtained
solutions of the crossing of the phantom divide under a quantum correction of
massless conformally-invariant fields and we have seen that quantum correction
could be small when the phantom crossing occurs and the obtained solutions of
the phantom crossing could be stable under the quantum correction. It has also
been noted that the potential increases as the matter-chameleon coupling gets
stronger with the evolution of the universe.
