  We follow to Witten proposal in the calculation of conformal anomaly from
d+1-dimensional higher derivative gravity via AdS/CFT correspondence. It is
assumed that some d-dimensional conformal field theories have a description in
terms of above d+1-dimensional higher derivative gravity which includes not
only Einstein term and cosmological constant but also curvature squared terms.
The explicit expression for two-dimensional and four-dimensional anomalies is
found, it contains higher derivative corrections. In particular, it is shown
that not only Einstein gravity but also theory with the Lagrangian
$L=aR^2+bR_{\mu\nu}R^{\mu\nu} + \Lambda$ (even when a=0 or b=0) is
five-dimensional bulk theory for d=4 ${\cal N}=4$ super Yang-Mills theory in
AdS/CFT correspondence. Similar d+1=3 theory with (or without) Einstein term
may describe d=2 scalar or spinor CFTs. That gives new versions of bulk side
which may be useful in different aspects. As application of our general
formalism we find next-to-leading corrections to the conformal anomaly of
${\cal N}=2$ supersymmetric theory from d=5 AdS higher derivative gravity (low
energy string effective action).
