Based on previous studies, a finite-time observer of the linear singular time-delay systems is designed. First, Lambert W function and its character were discussed. On this basis, the condition of judging timedelay system′s stability and the observer which converges to state asymptotically were given. Second, using eigenvalue assigning technology based on Lambert W function, an easy and convenient way of resolving finite-time normal observers′ coefficient matrix was proposed. Finally, Matlab was used to simulate a practical exam, and the result proved that the design proposed in this paper was effective and efficient, and it could be applied well in linear singular time-delay systems.