The ordered crystalline Fe3Pt invar alloy is in a special magnetic critical state under which the lattice dynamic stability of the system is extremely sensitive to the external pressure. Using projection augmented plane wave method based on the density functional theory, we calculate the dependences of enthalpy and magnetism of different crystalline alloys of Fe3Pt on external pressure. The results reveal that the P4/mbm structure is thermodynamically stable under pressures below 18.54 GPa. The total magnetic moments of Pm3m, I4/mmm and DO22 structures decrease rapidly and oscillate near the ferromagnetic collapse critical pressure. Furthermore in I4/mmm and DO22 structures the atomic magnetic moment of Fe1 reverses near the critical pressure. At a pressure of 43 GPa, the micro-ferrimagnetic property in DO22 structure becomes apparently strengthened while its volume increases rapidly. The lattice dynamic calculation shows that the spontaneous magnetization of the system in ferromagnetic states induces the softening of the transverse acoustic phonon TA1(M) in the Fe3Pt of Pm3m structure, and there exists a strong spontaneous volume magnetostriction at pressures below 26.95 GPa. Especially, in the pressure range between the ferromagnetic collapse critical pressure 41.9 GPa and the magnetism completely disappearing pressure 57.25 GPa, the lattice dynamic stability is more sensitive to the pressure. The pressure induces the stability of the phonon spectrum of the system at pressures above 57.25 GPa.