  In this paper, we present an exponential modification for the action of an
AdS black hole in the absence of a matter field. An approximated black hole
solution is obtained up to the third order of perturbation coefficient. A
thermodynamic investigation in canonical ensemble shows that the behavior of a
Van der Waals fluid is not seen in this model. Nevertheless, the study of
thermodynamic potentials and other related quantities suggests that the
thermodynamic phase transitions of the first and second types can occur in this
model. The forms of the phase transitions are more similar to the Hawking-Page
phase transitions.
