  We study the thermodynamics of $D$-dimensional Born-Infeld AdS black holes in
the extended phase space. We find that the usual small-large black hole phase
transition, which exhibits analogy with the Van de Waals liquid-gas system
holds in all dimensions greater than three. However, different from the
four-dimensional case, in the system of higher dimensional Born-Infeld AdS
black holes there is no reentrant phase transition. For the three-dimensional
Born-Infeld AS black hole, there does not exist critical phenomena.
