This paper investigates the decay rates of continuous-time singular systems with unbounded delays. By introducing an auxiliary system for the original system, the positivity and asymptotic stability conditions of the system are investigated first. Then, µ-stability criteria, which are applied to characterize the decay rates of the systems, are proposed, and the relation between the system matrices and µ-stability is studied. Those results include the stability of positive singular systems with bounded time-varying delays and time-varying delays with linear growth rate as special cases. Finally, a numerical example is given to illustrate the obtained theoretical results.