This paper investigates the robust sliding mode control (SMC) problem for a class of uncertain switched systems with time-varying delay. The sliding surface is constructed such that the sliding motion is completely invariant to all admissible uncertainties. For the case of the known delay-derivative upper bound, by using the multiple Lyapunov functions method, the Hysteresis switching law dependent on the state and the previous value of switching signal are designed to stabilize the sliding motion and avoid the chattering. Variable structure controllers are developed to drive the state of switched systems to reach the sliding surface in finite time and remain on it thereafter. For the case of the unknown delay-derivative upper bound, based on the single Lyapunov function method, the conditions of stabilization are obtained. Finally, a numerical example is given to illustrate the effectiveness of the proposed methods.