Abstract The electronic structure and magnetic properties of the Laves phase of LuFe 2 with C14, C15, and C36 structures has been investigated using the full-potential linearized augmented plane wave method. In order to study the stability of magnetic phases, nonmagnetic and spin-polarized calculations for ferromagnetic ordering were performed. It is found that the ferromagnetic hexagonal C14 phase is the ground-state structure and the C15 phase is an intermediate state between the C14 and C36 structures. There is an increase in the average magnetic moment on the Fe sites in the order of C15 →C14 →C36 structures, whereas the Lu-moment is not significantly different. We also find that there exist both localized and itinerant d electrons, resulting in antiferromagnetic ordering in the three structures. Their density-of-states, equilibrium volumes, and elastic properties are discussed, which is important for the understanding of the physical properties of LuFe 2 and may inspire future experimental research.