The electronic structure and optical properties of UO2 are investigated using the first principles density functional method within local-spin density approximation (LSDA), and the Coulomb correlation energy (U) is used to calculate the lattice constant, energy band structure and optical properties of UO2. The calculated lattice constant is 5.40 ?, and the band gap is 1.82 eV. We succeeded in predicting the correct anti-ferromagnetic insulating ground state of uranium dioxide. By analyzing the energy structure and dielectric function, we find that in uranium ions the 6d band splits into two sub-bands, which is in agreement with experimental results.