By using projection augmented plane wave method (PAW) and based on the density functional theory, the stability of lattice dynamics and the magnetism of ordered crystalline alloy -Fe4N are studied at high external pressures. In comparison with the phonon spectrum of -Fe4N without considering the spin-polarization, it is found that the ground-state lattice dynamics stability of the ferromagnetic phase -Fe4N is induced by the spontaneous magnetization at pressures below 1 GPa. The phonon spectra at point (0.37, 0.37, 0) in line , points X and M become softening at pressures between 1.03 and 31.5 GPa. The pressure-induced effect and the spontaneous magnetization effect on the atoms reach a stable equilibrium state at the pressures between 31.5 and 60.8 GPa, which result in the phonon spectrum stability. As the pressure exceeds 61.3 GPa, the system becomes more instable dynamically with the increase of the external pressure. The softening at point M of the acoustic phonon is treated by the soft-mode phase theory at 10 GPa, and a new dynamic stability high-pressure phase with a space group of P2/m is found. This new phase is thermodynamically stable and possesses the same magnetic moments as that of -Fe4N at pressures below 1 GPa. The enthalpy value of the phase P2/m is less than that of phase at the pressures between 2.9 and 19 GPa, therefore its ground-state structure is more stable. As the pressure exceeds 20 GPa, both phases possess almost the same magnetic moments.