The equilibrium structure, harmonic frequency and potential energy curves for two of the excited states a1Δg and b1Σ+g of O2 molecule were calculated by using MRCI method with aug-cc-pVQZ, cc-pV5Z, 6-311++g（d,p）and 6-311++g（3df,3pd） basis sets. The analytical potential energy functions for a1Δg and b1Σ+g of O2 was fitted by Murrell-Sorbie theory . The force constants and spectrum data were obtained according to fitted parameters. Results show that our results are good agreed with the experimental value.