This paper is concerned with the problem of asynchronous l(2)-l(infinity) filtering for discrete-time stochastic Markov jump systems with sensor nonlinearity. The sensor nonlinearity is assumed to occur randomly according to a stochastic variable satisfying the Bernoulli distribution. A sufficient condition is first given such that the resultant filtering error system, which is a kind of nonhomogeneous Markov jump system, is stochastically stable with a guaranteed l(2)-l(infinity) performance index. Then the existence criterion of the desired asynchronous filter with piecewise homogeneous Markov chain is proposed in terms of a set of linear matrix inequalities. A numerical example is given to show the effectiveness and potential of the developed theoretical results. (C) 2013 Elsevier Ltd. All rights reserved.