This paper addresses the exponential H_∞ filtering problem of asynchronous switched linear discrete-time systems with mode-dependent average dwell time(MDADT). In practical situation, the switching of the designed mode-dependent full-order filter often lags behind its corresponding subsystems. Therefore, the running time interval of the subsystem is divided into two parts: the matched and the mismatched. For these two parts, the full-order filter is designed using the MDADT and the mu dependent multi-Lyapunov function method, such that the global uniform exponential stability and exponential H_∞ performance of the asynchronous filtering error system are guaranteed. The sufficient conditions for the existence of the designed filter are given in terms of LMIs. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method.