The crystal structure, electronic structure and elastic constants of uranium dioxide are investigated using first-principles calculations, wherein the generalized gradient approximation and Hubbard U terms are used in the framework of density-functional theory. On-site Coulomb interactions with the simplified rotational invariant approach (the Dudarev approach), fully relativistic calculations for the coreflelectrons (repreflented as a pseudopotential), and scalar relativistic approximations for the valence electrons areflemployed to account for the relativistic effects and electron correlation of 5f electrons in UO2. The Hubbard U parameters (Ueff=U-J, U=3.70 eV, J=0.40 eV) are derived by calculating the band gap width of UO2. In addition, the electron density of states calculation suggests that the following value of band gap is appropriate. The calculated lattice constant is 5.54 Å, and the band gap width is 2.17 eV which shows that UO2 is a semiconductor. Its density of states shows that the U 5f orbital contributes to the peaks immediately adjacent to the Fermi level, which agrees with the U 5f2 configuration, while the O 2p orbital plays a dominant role in the bonding band at approximately -6 to -2 eV. Results obtained above have been compared with available experimental data, and also discussed in relation to previous calculations. Above results are better than existing ones gained by others. Analyzing the density of states for different Hubbard U parameters, we find that the Hubbard U parameters can influence the distribution of U 5f electronic orbit.