This paper deals with the problem of singular linear quadratic performance with the worst-disturbance rejection for descriptor systems. Under the conditions we give, the worst-disturbance and the optimal control-state pair are unique respectively, the optimal control can be synthesized as state feedback and the closed-loop system is regular, stable and impulse-free. This paper deals with the problem of singular linear quadratic performance with the worst-disturbance rejection for descriptor systems. Under the conditions we give, the worst-disturbance and the optimal control-state pair are unique respectively, the optimal control can be synthesized as state feedback and the closed-loop system is regular, stable and impulse-free.