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 deter-mined 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 $1.72mu_B$compared to the unrelaxed case ($2.39mu_B$). 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.