The problem of observer-based robust predictive control is studied for the singular systems with norm-bounded uncertainties and time-delay,and the design method of robust predictive observer-based controller is proposed.By constructing the Lyapunov function with the error terms,the infinite time domain“min-max”optimization problems are converted into convex optimization problems solving by the linear matrix inequality (LMI),and the sufficient conditions for the existence of this control are derived.It is proved that the robust stability of the closed-loop singular systems can be guaranteed by the initial feasible solutions of the optimization problems,and the regular and the impulse-free of the singular systems are also guaranteed.A simulation example illustrates the efficiency of this method. The problem of observer-based robust predictive control is studied for the singular systems with norm-bounded uncertainties and time-delay, and the design method of robust predictive observer-based controllers is proposed. By constructing the Lyapunov function with the error terms, the infinite time domain “min-max ” optimization problems are converted into convex optimization problems solved by the linear matrix inequality (LMI), and the sufficient conditions for the existence of this control are derived. It is proved that the robust stability of the closed-loop singular systems can be guaranteed by the initial feasible solutions of the optimization problems, and the regular and the impulse-free of the singular systems are also guaranteed. A simulation example shows the efficiency of this method.