— For linear singular time-delay systems, the most existing results focus on the simple case, i.e. E ˙ x(t) = A 0 x(t) + A 1 x(t − τ). Few results have been stated for the general linear singular time-delay systems of the form ∑ l i=0 E i ˙ x(t − iτ) = ∑ k i=0 A i x(t − iτ), which covers also neutral delay systems. For such a general case, this paper deduced sufficient conditions, with which a simple Luenberger-like observer can be designed in order to exponentially estimate the states.