This paper investigates the problem of observer design for a general class of linear singular time-delay systems, in which the time delays are involved in the state and its derivatives, the output and the known input (if there exists). The involvement of the delay could be multiple which however is rarely studied in the literature. Sufficient conditions are proposed which guarantees the existence of a Luenberger-like observer for the general system. (C) 2017 Elsevier Ltd. All rights reserved.