We performed first-principles calculations for the pressure-induced martensitic phase transition from the ground state ferromagnetic bcc phase to a nonmagnetic hcp phase in Fe under hydrostatic and non-hydrostatic pressure based on density-functional theory, employing the pseudopotentional and plane-wave method. The calculated results show that the magnetic moment of bcc iron under non-hydrostatic conditions decreases faster than that under hydrostatic conditions as the stress increases from 0 GPa to 18 GPa. Theoretical calculations prove that non-hydrostatic conditions can significantly reduce the bcc phase to hcp phase transition pressure. The critical stress for bcc-to-hcp transformation decreases linearly as the non-hydrostatic effect increases. The physical origins of the influence of non-hydrostatic pressure on the transition pressure are discussed.