Equilibrium structure geometries and stability of the epoxide [6,6] and open [C60O] isomers of C60O as well as rearrangement paths between the two isomers were determined using the second-order Moller-Plesset perturbation theory (MP2) and hybrid density functional theory (DFT, B3LYP and B3PW91) methods. It is manifested that the geometrical parameters involved in oxygen binding in C60O and relative stability between the [6,6] and [5,6] isomer of C60O have a strong dependence on basis set and electron correlation treatment, and it is important to employ an appropriate basis set and correlation level to correctly predict the equilibrium,geometries and stability of the [6,6] and [5,6] isomers of C60O. For large enough basis sets at proper correlated levels such as the MP2 and B3PW91 DFT methods, the [6,6] isomer is found to be more stable than the [5,6] isomer, in contrast to previous semiempirical and low-level ab initio studies. The stability of the 16,6] form over the [5,6] form also appears to be derived from the difference in vibrational motions between the two isomers. It is also found that there appears to exist only one transition state connecting the two isomers, and rearrangement from the [6,6] isomer to the [5,6] isomer occurs via this transition state in a single step, although the barrier height appears to be rather high. A comparison of the simulated IR absorption spectra of the [6,6] and [5,6] form at the B3PW91/cc-pVDZ level with the experimental spectrum of C60O appears to Suggest the presence and near-isoenergeticity of the [6,6] and [5,6] isomer of C60O at low temperature, in accordance with the calculation results reported in this paper.