  The C-metric solution of conformal gravity with a conformally coupled scalar
field is presented. The solution belongs to the class of Petrov type D
spacetimes and is conformal to the standard AdS C-metric appeared in vacuum
Einstein gravity. For all parameter ranges, we identify some of the physically
interesting static regions and the corresponding coordinate ranges. The
solution may contain a black hole event horizon, an acceleration horizon,
either of which may be cut by the conformal infinity or be hidden behind the
conformal infinity. Since the model is conformally invariant, we also discussed
the possible effects of the conformal gauge choices on the structure of the
spacetime.
