This paper is concerned with the problem of distributed H∞ filtering for discrete-time sensor networks with/without asymmetric intercommunication delays. Combining with the Kronecker product, a refined technique is provided to realize the complicated decoupling between the specifical sensor node and its underlying neighboring ones in the presence of intercommunication delays. Based on a previous bounded real lemma, a sufficient and necessary condition on distributed H∞ filter design without delays is provided. For the case with asymmetric intercommunication delays, a sufficient condition is established for the existence of such distributed H ∞ filters that render the resulting filter error system asymptotically stable under which a prescribed disturbance attenuation performance index is guaranteed. The filter design problem is posed in terms of linear matrix inequalities (LMIs). The Leslie model which describes a certain pest's structured population dynamics is finally presented to show the effectiveness and feasibility of the developed theoretical results.