An $H{infty}$ controller with a roll eccentricity filter is proposed to alleviate the effect of entry thickness variation and roll eccentricity occured in rolling stands themselves of tandem cold mills. A robust controller to the disturbances is designed by H$_{infty}$ control techniques, which can reflect the input direction of disturbances and the knowledge of disturbance spectrum in the frequency domain. First, fundamental problems in tandem cold mills such as process transport delay inherent in the exit thickness measurement and the feedforward loading of roll eccentricity signals on the exit thickness be overcome by the roll eccentricity filtering and the compensation for the error of gaugemeter thickness estimator. And non-satndard $H{infty}$ control problem caused by the selection of weighting function having poles on the $J{omega}$-axis is discussed. The resultant controller composed by an $H{infty}$ controller and an estimator for the roll eccentricity is evaluated through computer simulations. The effectiveness of the proposed control method is compared to that of the conventional LQ controller method and a feedforward controller for the roll eccentricity, which has been already studied.