At a switching point, the inconsistency can exist between subsystems switched before and after the point, resulting in the solutions of singular switched system with time delay there may be discontinuity. We consider the discontinuity of the solutions for a class of switched linear singular systems with time delay and the convergence of discontinuous solutions. Using Lyapunov-Krasovskii function and the LMI method, we establish some criteria to guarantee all solutions of the systems converge to zero. The criteria are expressed as LMI form and depended time delay. An example is given to illustrate the application of the presented results.