An analytical potential energy function for the ground state 3Σ+u of UO2 has been derived using many-body expansion method. The present paper correctly determines the dissociation limits, based on group theory and atomic and molecular reactive statics (AMRS). Using the MP2 (The HF calculation followed by a second-order Moller-Plesset correlation) of Gaussian94W and the RECP (the relativistic effective core potential) for U and basis 6-311G* for O,the present work has optimized the equilibrium geometry for the ground state 3Σ+u of UO2, which is linear O—U—O,whose equilibrium nuclear distance and dissociation energy are 0.17789nm and 14.1036eV.And the metastable structure U—O—O is discovered for the first time,to our knowledge,which is 5.7731eV higher than the stable structure.Then,the potential energy function is successfully used for describing the equilibrium geometry of UO2 and UOO,which is accurate enough in the whole region for dynamical research.