For input-delayed systems with time-varying uncertainties in industrial applications, a robust predictor based anti-disturbance control design is proposed in this paper based on only output measurement, which can be applied to improve system performance in the presence of constant, asymptotically stable, step, ramp, or harmonic type disturbances, typically encountered in engineering practice. A novel predictor, named state & disturbance observer-predictor (SDOP), is firstly introduced to estimate the 'delay-free' system state and disturbance dynamics simultaneously, with no need to store the control history as required in the existing predictor-based control methods. To allow for long input delay, another design of sequential SDOPs (SSDOPs) is proposed such that each SSDOP only needs to estimate the future system state and disturbance in terms of a specified step size for implementation. Moreover, a recursive sub-optimal Ho. design of SSDOPs is given such that the computation burden is independent of the number of SSDOPs and thus could be significantly reduced. Consequently, two anti-disturbance control schemes are developed based on an SDOP or SSDOPs to improve system performance. For the nominal system, the input delay is allowed to be arbitrarily long by increasing the number of SSDOPs. For the presence of time-varying plant uncertainties, asymptotic disturbance rejection performance can be achieved. A sufficient condition for robust stability of the closed-loop system is established in terms of matrix inequality, which can be effectively solved to determine the controller parameters. An illustrative example from the literature is used to demonstrate the effectiveness and merit of the proposed method. (C) 2019 Elsevier Ltd. All rights reserved.