Abstract 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 .