We present an ab initio calculation of interlayer magnetic coupling for Fe/Nb multilayers using the self-consistent full-potential linearized augmented-plane-wave (FLAPW) method. For this calculation, we have constructed supercells consisting of bcc Fe and Nb multilayers in Fe/Nb/Fe sandwich geometry stacked along (001) direction. In the supercells two Fe layers are separated by Nb layers ranging from 1 to 11 layers. We have calculated the total energy of the system as a function of Nb spacer layer thickness. For each spacer layer thickness, we have done three calculations corresponding to para, ferro and antiferromagnetic ordering of Fe atoms. The interlayer magnetic coupling is obtained from the energy difference of the systems in which Fe layers are antiferromagnetically and ferromagnetically ordered. We find that the interlayer magnetic coupling oscillates with increasing Nb spacer thickness in agreement with the experimental results. The induced magnetic moment is also found to be oscillating with increasing Nb spacer layer thickness.