We performed first-principles calculations for the pressure-induced martensitic phase transition from the ground state ferromagnetic body-center cubic (bcc) phase to a nonmagnetic hexagonal close-packed (hcp) phase of Fe under uniaxial strain along the ［001］ direction of bcc phase based on density-functional theory, employing the pseudopotentional and plane-wave method. The calculated results show that the transition path under unixial strain is significantly different from that under hydrostatic pressure. A sudden drop of the magnetic moment is observed at a critical point on the transition path, which results in a discontinuous derivative in the total energy and volume curve. This is a feature of a magnetic first-order phase transition, which indicates that magnetism is the primary stabilizing mechanism of the bcc structure. The enthalpy barrier for bcc-to-hcp transformation decreases as the uniaxial strain (the pressure) increases. The physical origin of the influence of uniaxial strain on the phase transition is discussed.