A state reconstruction problem is investigated for a class of discrete-time complex networks with the missing measurements in this paper. The different node dynamics and different inner coupling matrices are considered in the proposed complex networks. By using the Lyapunov stability theory combined with stochastic analysis, a novel state reconstruction scheme is proposed to estimate the states of discrete-time complex networks through the available output measurements, where the measurements are stochastic missing which are caused by data transmission among nodes due to communication unreliability. State reconstruction and stability conditions are derived in terms of linear matrix inequalities (LMIs). A simulation example is provided to demonstrate the effectiveness of the proposed scheme.