A new phase of C2/m OsN2 is proposed in this paper. The crystal structure, elasticity and electronic properties of C2/m OsN2 were studied by rst-principles calculations. The elastic constants, the elastic moduli (B, G, and E) and Poisson's ratio v of OsN2 have been investigated. From the rst-principles calculations, we nd that C2/m OsN2 is metallic and mechanically stable. The quasi-harmonic Debye model, using a set of total energy versus molar volume obtained from the rst-principles calculations, is applied to the study of the thermal and vibrational eects. The dependence of structural parameters, thermal expansions, heat capacities, Grüneisen parameters and Debye temperatures on the temperature and pressure are obtained in the whole pressure range from 0 to 80 GPa and temperature range from 0 to 800 K as well as compared with available data.