We use density functional theory to investigate several high-pressure polymorphs of Al2O3 and predict a new stable polymorph at high pressures with post-perovskite structure. The ambient pressure R$overline{3}$c corundum phase transforms to the Pbcn Rh2O3(II) structure at about 104 GPa. At about 156 GPa, the Rh2O3(II) structure transforms further to the Cmcm post-perovskite structure. The Al2O3 Pbnm perovskite structure is metastable at all pressures with respect to corundum, Rh2O3(II) and post-perovskite. The metastable perovskite to post-perovskite transition takes place at about 120 GPa, which is above the same transition in MgSiO3. Thus the presence of Al2O3 in the lower mantle, dissolved in MgSiO3 perovskite, will increase the transition pressure to post-perovskite. Our calculations also show that Al2O3 is most likely dissolved in the post-perovskite phase of MgSiO3, increasing its stability at high pressures.