In stochastic optimal control with a feedforward link, there are two problems, one is the difficulty of design by frequency-shaped cost functionals, the other is the problem that the level of the frequency response increases beyond the frequency range of an assumed disturbance dynamics. In this study, to overcome these defects of the stochastic vibration control, methods for design of frequency cost and robust control are presented by applying the theory of H^∞ control. In the numerical calculation using a single-degree-of-freedom system, the usefulness of the presented method using the H^∞ control was verified.