This paper is concerned with the H-infinity filtering problem for a general class of nonlinear discrete-time stochastic systems with randomly varying sensor delays, where the delayed sensor measurement is governed by a stochastic variable satisfying the Bernoulli random binary distribution law. In terms of the Hamilton-Jacobi-Isaacs inequalities, preliminary results are first obtained that ensure the addressed system to possess an l(2)-gain less than a given positive scalar gamma. Next, a sufficient condition is established under which the filtering process is asymptotically stable in the mean square and the filtering error satisfies the H-infinity performance constraint for all nonzero exogenous disturbances under the zero-initial condition. Such a sufficient condition is then decoupled into four inequalities for the purpose of easy implementation. Furthermore, it is shown that our main results can be readily specialized to the case of linear stochastic systems. Finally, a numerical simulation example is used to demonstrate the effectiveness of the results derived. (C) 2008 Elsevier Ltd. All rights reserved.