We present an iterative method to reconstruct the linear-theory initialconditions from the late-time cosmological matter density field, withthe intent of improving the recovery of the cosmic distance scale fromthe baryon acoustic oscillations. We present tests using the dark matterdensity field in both real and redshift space generated from an N-bodysimulation. In redshift space at z = 0.5, we find that the reconstructeddisplacement field using our iterative method are more than 80 per centcorrelated with the true displacement field of the dark matter particleson scales k < 0.10 h Mpc-1. Furthermore, we show that thetwo-point correlation function of our reconstructed density fieldmatches that of the initial density field substantially better,especially on small scales (<40 h-1 Mpc). Ourredshift-space results are improved if we use an anisotropic smoothingso as to account for the reduced small-scale information along the lineof sight in redshift space.