Transition metal nitride has many excellent physical and chemical properties and abundant crystal structure. But phase pure transition metal nitrides are difficult to be synthesized, which greatly limits the exploration of its characters. Using theoretical calculations can effectively predict many physical and chemical properties of materials, and giving guidance to workers engaged in experimental synthesis. In this paper, WC-structured MoN which may possess high hardness is studied systematically by theoretical calculation. In this paper, density of states (DOS), bulk modulus, shear modulus, Mulliken population and electron localization function (ELF) of MoN were calculated using first-principles calculations. Through the calculation above, it is found that the chemical bond between molybdenum atom and nitrogen atom in MoN shows covalency, which can result in high hardness. It is worth noting that MoN shows excellent conduction characteristics, demonstrating that MoN can be used in industry as a multiple.