Owing to its high thermal conductivity and uranium density, uranium nitride (UN) has great application prospects in various nuclear facilities. However, sintering is an important step during the preparation of UN fuel, and the properties of UN pellets in reactor are significantly affected by sintering parameters. Therefore, using numerical simulation techniques to investigate the sintering mechanism of UN fuel is of great significance. In this work, a UN sintering phase-field model based on grand potential is established, which simultaneously considers the rigid body motion of particles and the mass diffusion. This model enables the expansion of the interface width, thereby increasing the spatial scale of the simulation system. Firstly, a validation analysis of the constructed model is conducted. The phase-field variables are symmetrically distributed at the local equilibrium interface. The rigid body motion of particles significantly promotes the densification process. Subsequently, the sintering process of two particles is simulated at different temperatures. The results show that the growth of the sintering neck follows a power function relationship, with a power exponent n of 7.14, indicating that the dominant mass transfer mechanism is surface diffusion. As the sintering temperature increases, the sintering neck growth accelerates, and the maximum concentration of vacancies within the grain boundary increases. Finally, the multi-particle sintering is investigated at different temperatures. The contact and overlap between sintering necks form a complex grain boundary structure, and the internal pores transform from irregular to circular shapes. During densification, vacancies originating from pores separate into grain boundaries and then diffuse into the external gas phase or larger pores. The average pore size initially increases slowly and then remains stable. As the sintering temperature increases from 1723 K to 1873 K, the degree of densification progressively improves.