— This paper presents a new method to design observers for linear time-delay systems with unknown inputs both in the state and the output. In contrast to many observers, which normally estimate the system state in an asymptotic fashion, the proposed observer estimates the exact system state in a predetermined finite time. The finite-time observation is achieved by updating the observer state based on actual and past data of the observer. Simulation results are also presented to illustrate the convergence behavior of the finite-time observer.