The O-rich asymptotic giant branch (AGB) stars experience strong mass-loss with efficient dust condensation and they are major sources of dust in the interstellar medium. Alumina dust (Al2O3) is an important dust component in O-rich circumstellar shells and it is expected to be fairly abundant in the winds of the more massive and O-rich AGB stars. By coupling AGB stellar nucleosynthesis and dust formation, we present a self-consistent exploration on the Al2O3 production in the winds of AGB stars with progenitor masses between ˜3 and 7 M⊙ and metallicities in the range 0.0003 ≤ Z ≤ 0.018. We find that Al2O3 particles form at radial distances from the centre between ˜2 and 4 R* (depending on metallicity), which is in agreement with recent interferometric observations of Galactic O-rich AGB stars. The mass of Al2O3 dust is found to scale almost linearly with metallicity, with solar metallicity AGBs producing the highest amount (about 10-3 M⊙) of alumina dust. The Al2O3 grain size decreases with decreasing metallicity (and initial stellar mass) and the maximum size of the Al2O3 grains is ˜0.075 μm for the solar metallicity models. Interestingly, the strong depletion of gaseous Al observed in the low-metallicity hot bottom burning (HBB) AGB star HV 2576 seems to be consistent with the formation of Al2O3 dust as predicted by our models. We suggest that the content of Al may be used as a mass (and evolutionary stage) indicator in AGB stars experiencing HBB.