The results of the first LCAO DFT calculations of cohesive energy, band structure and charge distribution in uranium nitride (UN) crystal are presented and discussed. The calculations are made with the uranium atom relativistic effective core potentials, including 60, 78 and 81 electrons in the core. It is demonstrated that the chemical bonding in UN crystal has a metallic-covalent nature. Three 5f-electrons are localized on the U atom and occupy the states near the Fermi level. The metallic nature of the crystal is due to the f-character of both the valence-band top and the conduction-band bottom. The covalent bonds are formed by the interaction of 7s- and 6d-states of the uranium atom with the 2p-states of the nitrogen atom. It is shown that the inclusion of 5f-electrons in the atomic core introduces small changes in the calculated cohesive energy of UN crystal and electron charge distribution. However, the inclusion of 5s-, 5p-, 5d-electrons in the valence shell allows the better agreement with the calculated and experimental cohesive-energy value.