We have performed the density functional theory calculations of $UO_2$ using the spin-polarized generalized gradient approximation (SP-GGA) and the SP-GGA+U approach. The SP-GGA+U approach correctly predicts the insulating electronic structure with antiferromagnetic ordering, but the SP-GGA calculations predict metallic behavior. The cohesive properties obtained from the SP-GGA+U calculations are in good agreement with the available experimental results and previous calculations. The spin-polarized local density of states shows that the antiferromagnetic ordering of $UO_2$ is governed by 5f orbitals of uranium ion. Our calculations demonstrate that the strong correlation of U 5f electrons should be taken into account for a reliable description of $UO_2$ physics.