In this paper, the robust distributed filtering problem is investigated for a class of wireless sensor networks with stochastic parameter and topology uncertainties. The local filters collect information not only from itself but also from its neighbouring sensor nodes according to the network topology. A novel robust distributed filter is proposed which takes stochastic parameter and topology uncertainties into full consideration but does not depend on any specific structure of uncertainties. By proper designing of the filter gain, the trace of estimation error covariance is minimised at each time step, where the new stochastic analysis and augmentation transformation techniques are developed to handle the challenges resulting from multiplicative stochastic uncertainties and sparse topology. The corresponding recursive robust distributed filtering algorithm is also presented for real-time online applications. Finally, a simulation study is carried out to illustrate the effectiveness and applicability of our proposed method.