This paper is concerned with a new distributed H-infinity-consensus filtering problem over a finite-horizon for sensor networks with multiple missing measurements. The so-called H-infinity-consensus performance requirement is defined to quantify bounded consensus regarding the filtering errors (agreements) over a finite-horizon. A set of random variables are utilized to model the probabilistic information missing phenomena occurring in the channels from the system to the sensors. A sufficient condition is first established in terms of a set of difference linear matrix inequalities (DLMIs) under which the expected H-infinity-consensus performance constraint is guaranteed. Given the measurements and estimates of the system state and its neighbors, the filter parameters are then explicitly parameterized by means of the solutions to a certain set of DLMIs that can be computed recursively. Subsequently, two kinds of robust distributed H-infinity-consensus filters are designed for the system with norm-bounded uncertainties and polytopic uncertainties. Finally, two numerical simulation examples are used to demonstrate the effectiveness of the proposed distributed filters design scheme. (C) 2010 Elsevier Ltd. All rights reserved.