Limit of the Rayleigh scattering loss in Ge-doped silica core fiber was estimated from the results of structural relaxation and the Rayleigh scattering measurements, and the most suitable fiber-drawing condition to reduce the Rayleigh scattering loss was determined. An annealing furnace, which could be attached to a fiber-drawing tower, was developed for realizing the optimum fiber-drawing condition. Drawing tests with this furnace confirmed our estimation of the loss.