In this paper, we propose a new approach to an adaptive observer design for a class of multi-input-multi-output linear descriptor systems. Global exponential convergence for joint state-parameter estimation is established for noise-free systems. For noise corrupted descriptor systems, it is proved that the state and parameter estimation errors are bounded and converge in the mean to zero, when the noises are bounded and have zero means. Potential applications of the presented adaptive observer are online system identification, fault detection and adaptive control of descriptor systems. Numerical example is presented to illustrate the performance of the proposed adaptive observer. (C) 2013 Elsevier Ltd. All rights reserved.