This article studies reachable set estimation for discrete-time singular systems. By means of system decomposition and reconstruction, singular systems can be transformed into dynamic systems together with algebraic equations. Under this representation, two novel reachable set estimation methods based on ellipsoidal sets are proposed under nonzero initial conditions. A series of enclosing ellipsoidal sets can be obtained in two derived methods for bounding real-time states of the considered systems. Finally, the effectiveness of the proposed methods is illustrated with a numerical example.