This paper investigates the problem of robust stabilization of uncertain singular systems with time-varying delay in the presence of model uncertainties and input amplitude constraint. Here, the purpose of robust stabilization is to design a saturated state feedback such that the closed-loop system is regular, impulse free and stable for all admissible uncertainties. The timedelay has been considered to be time-varying with known lower and upper bound. The problem of stabilization is studied in two cases. First, the robust stabilization problem is considered for the singular systems with time-varying delay in the presence of actuator saturation and model uncertainties. In this case, the existence conditions of robust stabilizing delay-independent state feedback controller are given via the linear matrix inequalities. Additionally, an estimation of the domain of attraction of the closed-looped system is proposed in the related theorem. In the second case, delay-dependent criteria for robust stability of uncertain time-delay singular systems withconstrained input is given in two theorems. These theorems investigate delay-independent stability conditions via the linear matrix inequalities for constant and time-varying delay. Also, the domain of attraction for the closed-looped system is estimated in this case, too. Finally, practical and numerical examples are given and simulation results verify the theoretical achievements of paper.