In this article, we address the problem of designing an observer for a class of nonlinear time delay systems in descriptor form, in both discrete-time and continuous-time cases. We propose an observer design method using a particular Lyapunov function that leads to solve a linear matrix inequality condition ensuring the H-infinity convergence of the estimation error. Indeed, we use a Lyapunov function depending on the disturbances in order to avoid a specific obstacle in the stability analysis. Finally, three numerical examples are provided in order to show the validity of the proposed method.