Due to sensor indirect failure, signal bandwidth limitation and other reasons, measurement data missing and distributed delays become common phenomena in wireless sensor networks. System performance cannot be guaranteed if the effects on the system can not be considered effectively. The problem of H_∞ filtering for a class of discrete-time switched systems with distributed delays and random measurement data missing is studied. Bernoulli random sequence with known probability is used to describe the measurement data missing, and the filtering error system is then discussed by constructing a Lyapunov-krasorskii functional. The sufficient condition for guaranteeing the mean square exponential stability and the H_∞ performance of filtering error system is given by using the average dwell time method and LMI technique. The numerical simulation results show the feasibitity of the proposed method.