In this paper we consider the input delay compensation of linear systems with both state and input delays. Under the condition that the open-loop time-delay systems in the absence of input delay can be stabilized by (delayed) state feedback, a nested predictor based approach is established to predict the future states so that the delays in the input are compensated. It is shown that the compensated closed-loop system in the presence of input delay possesses the same characteristic equation as the closed-loop system in the absence of input delay. The proposed approach can be generalized to general linear systems having multiple state delays and/or multiple input delays. To implement the nested predictor based controllers by applying numerical integration approaches, an augmented nested predictor based approach by adding input filters is proposed. Two numerical examples are worked out to show the effectiveness of the proposed approach. (c) 2014 Elsevier Ltd. All rights reserved.