The structural and electronic properties of Pu2On (n = 1-8) molecules have been systematically studied within the screened hybrid density functional theory. On the basis of the calculations, plutonium and oxygen generally prefers forming Pu-O and Pu-O-Pu bonds over to Pu-Pu or O-O bonds. In the ground-state geometries, we find that the highest oxidation state for plutonium atoms is Pu(VI). Through fragmentation studies, we find that the Pu2O and Pu2O2 molecules are energetically stable among all studied compounds. When fixing the Fermi level to be energy zero, the Pu-5f states always distribute at the two sides of the Fermi level. With increasing the number of oxygen atoms and the oxidation state of plutonium, the Pu-6d states shift down from above to below the Fermi level.