In this contribution we investigate the input delay compensation for neutral type time-delay systems with both state and input delays. A nested predictor is established to predict the future states such that the input delay that can be arbitrarily large yet bounded are compensated completely. 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. An implementation scheme by adding input filters is also proposed. Under an additional assumption, explicit nested predictor feedback controllers involving only 1-fold integrals are established. A numerical example is carried out to support the obtained theoretical results. (C) 2016 Elsevier Ltd. All rights reserved.