Much interest in magnetic tunnel junctions (MTJs) with a perpendicular magnetic easy axis [perpendicular magnetocrystalline anisotropy (PMA)], consisting of ferromagnetic 3d transition- metal thin films with a MgO barrier, has rapidly increased in ultrahigh density and nonvolatile spin-electronics. Currently, efforts for searching promising PMA materials have remained a great challenge. Remarkably, recent findings of the PMA at Fe/MgO and CoFeB/MgO interfaces, where a weak Fe d(z2)-O p(z) hybridization at the interface enhances the PMA, have led to an important avenue toward the successful MTJ devices with the PMA. In the present search for PMA materials, the MA of Fe-based transition-metal thin films, consisting of only magnetic 3d elements of Mn, Fe, Co, and Ni, was systematically investigated by first principles calculations, and we found that giant PMA can be achieved by tuning the atomic-layer alignments in an Fe-Ni film, where a bcc-like-layer stacking alignment leads to the PMA thorough the spin-orbit coupling between occupied and unoccupied Ni d(x2-y2,xy) bands crossing the Fermi level. Thus, a promising 3d transition-metal thin film for the MgO-based magnetic tunnel junctions with the giant PMA was thus demonstrated.