  We present a new family of charged C-metrics in ${\cal N}=2$ gauged
supergravity in four dimensions. The double Wick rotation of the C-metric
allows us to bring our solution into a different family of the C-metrics
previously found by L\"u and V\'azquez-Poritz. In the case of zero acceleration
limit, our solution with vanishing charges reduces to the scalar haired black
holes in AdS with regular horizons. Nevertheless, it turns out that each family
of neutral solutions fails to veil the curvature singularity by the event
horizon, showing that neither of them represents the accelerated black holes
with a scalar hair. Physical solutions without visible curvature singularities
are obtained only in the case of nonvanishing charges. Causal structures of the
solution are spelled out in detail. We also present conditions under which the
solution preserves supersymmetry.
