The paper deals with the robust H-infinity control problem for uncertain linear systems with multiple state delays. The parameter uncertainties are time varying and unknown, but are norm-bounded, and the delays are time varying. Based on the LMI approach, a new method for designing a robust memoryless state feedback control law is proposed to stabilise this class of uncertain time-delay systems, and to reduce the effect of the disturbance input on the controlled output to a prescribed level for all admissible uncertainties. The results depend on the size and the varying rate of the delays and may be less conservative.