The geometric configuration, electronic structures and vibrational frequency of the AlxOy(x=1—2,y=1—3) molecules were calculated with B3LYP method at 6-311++g** level. The calculations show that the ground states of AlxOy molecules can be rapidly obtained by adding one or two O atoms to the different positions of Oy clusters with the aid of the software Gaussview 3.7, and taking into account of possible symmetries. Analysis of the geometrical parameters of ground state structure reveals that the atoms have chained or planar structure only. Analysis of the energy of ground state structure shows that Al atoms tend to bind with three other atoms. With one Al atom in the molecule the ground state structures multiplicity is two, with two Al atoms in the molecule, the ground state structures multiplicity is one except for Al2O3, of which the ground state structures multiplicity is three.