In this paper, we design a H^infty servo controller for gauge control of tandem cold mill. To improve the performance of the AGC(Aotomatic Gauge Control) system based on the Taylor linearized model of tandem cold mill, the H^infty servo controller is designed to satisfy robust stability, disturbance attenuation and robust tracking properties. The H^infty servo controller problem is modified as an usual H^infty control problem, and the solvability condition of the H^infty servo problem depends on the solvability of the modified H^infty control problem. Since this modified problem does not satisfied standard assumptions for the H^infty control problem, it is solved by an LMI(Linear Matrix Inequality) technique. Consequently, the comparison between the H^infty servo controller and the existing PID/FF(FeedForward) controller shows the usefulness of this study.