UN is a candidate fuel for light water reactors and fast reactors due to its high density, high thermal conductivity, and high melting point. The highly densified UN particles are desirable to strengthen the fuel structure and delay the release of fission gas. However, the mechanism of densification during sintering is still unclear from the view point of existing experimental results. Therefore, it is essential to simulate the densification process during sintering using the phase-field (PF) method. In the present work, the rigid body action of translation and rotation was introduced in the PF model. This work analyzed the effects of the advection flux of rigid body motion on the formation of the sintered neck, the equilibrium dihedral angle, and the densification during sintering. The simulation results showed that the introduction of advection flux of rigid body motion accelerated the formation of the sintering neck in the early stage of sintering, while such an effect was not obvious in the later stage. The equilibrium dihedral angle of the model with advection flux was consistent with that of the model, which only contained surface diffusion. The densification stomatal shrinkage was divided into three stages: surface diffusion dominated stage, advection flux dominated stage, and final densification progress. The increase in translational mobility accelerated the densification speed and increased the final density after densification, although this effect reached saturation after a certain threshold. Stable trigeminal grain boundaries (GBs) with 120° were formed when densification was completed. The characteristics of the sintered morphology of polycrystalline UN, such as trigeminal GBs, pore shrinkage, and densification, were consistent with the experimental results.