  We study the thermodynamic properties and critical behaviors of the
topological charged black hole in AdS space under the consideration of the
generalized uncertainty principle (GUP). It is found that only in the spherical
horizon case there are Van der Waals-like first-order phase transitions and
reentrant phase transitions. From the equation of state we find that the
GUP-corrected black hole can have one, two and three apparent critical points
under different conditions. However, it is verified by the Gibbs free energy
that in either case there is at most one physical critical point.
