  Considering the power-law corrections to the black hole entropy, which appear
in dealing with the entanglement of quantum fields inside and outside the
horizon, the holographic energy density is modified accordingly. In this paper
we study the power-law entropy-corrected holographic dark energy in the
framework of Brans-Dicke theory. We investigate the cosmological implications
of this model in detail. We also perform the study for the new agegraphic dark
energy model and calculate some relevant cosmological parameters and their
evolution. {As a result we find that this model can provide the present cosmic
acceleration and even the equation of state parameter of this model can cross
the phantom line $w_D=-1$ provided the model parameters are chosen suitably}.
