In this paper, we design a finite-time H_∞ observer. The system under consideration is a linear descriptor system subject to time-varying norm bounded disturbances. The aim of this paper is focused on the design of a state observer which ensures that the estimation error is finite-time bounded and minimizes the effect of the disturbances. A non bias condition is presented for the solvability of this problem, which is reduced to a problem involving linear matrix inequalities (LMIs). Finally, a numerical example is given to show the validity of the proposed methodology.