We present a study of the thermodynamic properties of ferromagnetic FeN phase with nickel arsenide structure in the frameworks of the density functional perturbation theory and generalized gradient approximation (GGA). Discussion of the thermodynamic properties of FeN is given with respect to the effect of external hydrostatic pressure applying. The pressure-induced enhancement of Debye temperature is predicted. The vibration densities of states at different pressures calculated by DFPT approach show the phonon band gap opening at pressure 50 GPa.