we study the issue of reachable set estimation for discrete-time singular neural networks with time-varying delays. By combining different methods and technologies including constructing a LKF, applying Jensen's and the reciprocally convex inequalities. The feasibility of solving the reachable set estimation solution of the described system is proved. A strictly proved theorem is proposed based on the linear matrix inequalities (LMIs), a theorem that can obtain the feasible solution of the resolved problem is proposed, the theorem establishes a sufficient condition to demonstrate that the elliptical region can constrain all states of the considered system, and this region is obtained considering input disturbances and zero initial conditions. In the end, we select specific system parameters and carry out a numerical simulation.