Abstract The crystal structural, elastic and thermodynamic properties of δ-WN under pressure are investigated by using the first-principles. The ground states properties are found to agree with the available experimental data and other theoretical results. The elastic constants, shear modulus and Young׳s modulus under pressure are calculated; the results show that the δ-WN is mechanically stable, which is consistent with the experiments data by Wang [Wang et al., Chem. Mater. 24 (2012) 3023] and the theoretical results by Yu [Yu et al., J. Alloys Compd. 487 (2009) 556]. The ductility of δ-WN was analyzed using the B/G ratio and Poisson׳s ratio σ. Finally, thermodynamic properties have been predicted, the results show that the Debye temperature, melting point and the minimum thermal conductivity increases when the pressure is increased, while specific heat coefficient γ decreases with increasing pressure.