  The near horizon geometry of the rotating C-metric, describing accelerating
Kerr-Newman black holes, is analysed. It is shown that, at extremality, even
though not it is isomorphic to the extremal Kerr-Newman, it remains a warped
and twisted product of $AdS_2 \times S^2$. Therefore the methods of the
Kerr/CFT correspondence can successfully be applied to build a CFT dual model,
whose entropy reproduce, through the Cardy formula, the Beckenstein-Hawking
entropy of the accelerating black hole. The mass of accelerating Kerr-Newman
black hole, which fulfil the first law of thermodynamics, is presented. Further
generalisation in presence of an external Melvin-like magnetic field, used to
regularise the conical singularity characteristic of the C-metrics, shows that
the Kerr/CFT correspondence can be applied also for the accelerating and
magnetised extremal black holes.
