The density function (B3LYP) method has been used to optimize the possible ground-state structures of AlO2 and Al2O molecules. The results show that the ground state of AlO2 molecule has D∞h symmetry and is in the X2Πu state. The parameters of structure are RAl-O=0.1661 nm and De=8.9217eV, respectively. The results also show that the ground state of Al2O molecule has D∞h symmetry and is in the X1Σg state. The parameters of structure are RO-Al=0.1731 nm and De=10.5269eV, respectively. The potential energy functions of AlO2 and Al2O have been derived from the many-body expansion theory. The contours describe correctly the configurations and the dissociation energies of the two ground-state molecules.