This paper considers the H-infinity-controller design problem for linear systems with time-varying delays in states, The authors obtain sufficient conditions for the existence of HX controllers in terms of three linear matrix inequalities (LMI＇s). These sufficient conditions are dependent on the maximum value of the time derivative of time-varying delay. Furthermore, they briefly explain how to construct such controllers from the positive-definite solutions of their LMI＇s and give an example.