The asynchronous H∞ filtering of discrete-time switched linear systems with missing measurement was investigated.The missing measurement from sensors could be described with Bernoulli distribution

where missing probability was a given constant.By using switched Lyapunov function and average dwell time method

some sufficient conditions of exponential mean square stability were obtained in forms of linear matrix inequalities for the filtering error system

in which the given missing measurement was of H∞.An exponentially mean square stable H∞ filter was designed and a numerical example was provided to show the effectiveness of the proposed approach.