The effects of surface relaxation on surface and interface magnetism in Fe / Cr (001) are investigated using the highly precise all-electron total-energy full-potential linearized augmented plane wave method. The Fe-Cr interlayer spacing is determined by total-energy calculation and it is found to be relaxed downward by 18 %. For the relaxed system, the magnetic moment of surface Fe is highly suppressed to be 1.72 μ_B compared to the unrelaxed case (2.39 μ_B). This reduction of magnetic moment is considered as a result of the enhanced hybridization between Fe-d and Cr-d states, which can be seen from the calculated density of states. This work suggests the importance of effect of relaxation to the surface and interface magnetism in Fe / Cr system.