This paper presents a novel Time Shift Approach for actuator fault reconstruction of systems with output time-delay based on a sliding mode observer (SMO). Arbitrary output delay duration, possibly uncertain and time-varying, can be considered. Ideal sliding mode is made possible even in the presence of delay. This is particularly important since chattering problems can be circumvented so that the proposed approach is conveniently applicable to the case of sampled-output systems. In order to allow a smooth fault reconstruction using noncausal filters, an intentional output delay of one or more sampling periods is introduced. Numerical simulations illustrate the effectiveness of the proposed methodology. (C) 2019 Elsevier Ltd. All rights reserved.