  We consider the effects of higher curvature terms on a holographic dual
description of boundary conformal field theory. Specifically, we consider
three-dimensional gravity with a specific combination of Ricci tensor square
and curvature scalar square, so called, new massive gravity. We show that a
boundary entropy and an entanglement entropy are given by similar expression
with those of the Einstein gravity case when we introduce an {\it effective}
Newton's constant and an {\it effective} cosmological constant. We also show
that the holographic g-theorem still holds in this extension, and we give some
comments about the central charge dependence of boundary entropy in the
holographic construction. In the same way, we consider new type black holes and
comment on the boundary profile. Moreover, we reproduce these results through
auxiliary field formalism in this specific higher curvature gravity.
