  In this paper, the Hawking-Page phase transitions between the black holes and
thermal anti-de Sitter (AdS) space are studied with the Gauss-Bonnet term in
the extended phase space, in which the varying cosmological constant plays the
role of an effective thermodynamic pressure. The Gauss-Bonnet term exhibits its
effects via introducing the corrections to the black hole entropy and Gibbs
free energy. The global phase structures, especially the phase transition
temperature $T_{\rm HP}$ and the Gibbs free energy $G$, are systematically
investigated, first for the Schwarzschild-AdS black holes and then for the
charged and rotating AdS black holes in the grand canonical ensembles, with
both analytical and numerical methods. It is found that there are terminal
points in the coexistence lines, and $T_{\rm HP}$ decreases at large electric
potentials and angular velocities and also decreases with the Gauss-Bonnet
coupling constant $\alpha$.
