  We study the thermal phase transitions of charged black holes in
dimensionally continued gravity in anti-de Sitter space. We find the van der
Waals-like phase transition in the temperature-entropy plane of the black holes
with spherical horizons in even dimensions, and there is no such phase
transition of the black holes with flat and hyperbolic geometries. Near the
critical inflection point, the critical exponent is computed and its value does
not depend on the dimension. The Maxwell equal area law is checked to be
fulfilled in the temperature-entropy diagram for the first order phase
transition. In odd dimensions, there are no thermal phase transitions for the
black hole with any geometry of the horizon.
