First-principles calculations are used to investigate the phase stability and martensitic transformation of two new all-d-metal Heusler alloys Fe2VIr and Fe2TaIr at 0–50 GPa. The difference in phase stability between Fe2VIr and Fe2TaIr is due to the effect of d-d orbital hybridisation between different atoms and the appearance of triply degenerate in the pressure-induced phonon optical modes. The softening behaviour of the transverse phonon mode along the high symmetry point X is responsible for the martensitic transformation of Fe2TaIr. We also observed the softening of the shear elastic constant C′ = (C11-C12)/2. Strong Fe-Fe magnetic coupling, softening of transverse acoustic phonon modes and anomalous softening of C′ awaken the martensitic transformation. Low-frequency phonon hybridisation of the heavy elements Ta and Ir is the driving force behind the softening. A surprising phenomenon is found during tetragonal deformation of the structure of Fe2TaIr at 45 GPa, whereby the structure break through the energy barrier of the leap and produced a tetragonal martensitic phase with a much lower energy. It may imply that pressure-induced Fe2TaIr produced a premartensitic phase. This work presents a detailed analysis of the anomalous softening behaviour of Fe2TaIr and the mechanism of the pressure-induced martensitic transformation. A new idea is proposed for an in-depth study of the martensitic phase transition precursor reaction.