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The robust stability problem of linear discrete singular time-delay systems with structured (elemental) parameter uncertainties is investigated. Under the assumptions that the nominal discrete singular time-delay system is regular, impulse-free and asymptotically stable, some new sufficient conditions are proposed to preserve the assumed properties when structured (elemental) parameter uncertainties are added into the nominal discrete singular time-delay system. Further new sufficient conditions are also proposed for guaranteeing that the linear discrete singular time-delay system with both structured (elemental) and unstructured (norm-bounded) parameter uncertainties has the properties of regularity, impulse-immunity and asymptotic stability. Four examples are given to demonstrate the applicability of the proposed sufficient conditions.