This paper deals with H_∞ control attenuating initial-state uncertainties, and its application to a magnetic suspension system. H_∞ control problem, which treats as a mixed attenuation of disturbance and initial-state uncertainty for linear time-invariant systems in the infinite-horizon case, is examined. The mixed attenuation supplies H_∞ controls with good transients and assures H_∞ controls of robustness against initial-state uncertainty. We apply this method to a magnetic suspension system, and evaluate attenuation property of the proposed disturbance and initial-state uncertainty via simulations and experiments.