  We construct some classes of electrically charged, static and spherically
symmetric black hole solutions of the four-dimensional
Einstein-Born-Infeld-dilaton gravity in the absence and presence of
Liouville-type potential for the dilaton field and investigate their
properties. These solutions are neither asymptotically flat nor (anti)-de
Sitter. We show that in the presence of the Liouville-type potential, there
exist two classes of solutions. We also compute temperature, entropy, charge
and mass of the black hole solutions, and find that these quantities satisfy
the first law of thermodynamics. We find that in order to fully satisfy all the
field equations consistently, there must be a relation between the electric
charge and other parameters of the system..
