This paper is concerned with the reachable set estimation (RSE) problem for singular systems with both time-varying delays and bounded peak disturbances. The objective is to search a bounded set that contains all the system states under zero initial conditions. By utilizing the theory of {1}-inverse and Wirtinger-based integral inequality, an improved criterion is established in terms of the linear matrix inequalities (LMIs) to guarantee that the reachable set of time-varying delay singular system is regular, impulse-free and bounded by the intersection of ellipsoids. Here, a relaxed Lyapunov-...