This article addresses the prediction-based distributed filtering problem for a class of time-varying nonlinear stochastic systems with communication delays and missing measurements through the sensor networks. The phenomenon of the missing measurements is depicted by a set of Bernoulli distributed random variables, where each sensor node possesses its own missing probability. The communication delays are taken into account, which commonly occur during the estimation exchanges among the sensor nodes with communication links. A new prediction-based suboptimal distributed filter is designed by taking the missing probabilities and the prediction estimation into account, which has the advantages on the active compensation of the impacts caused by the missing measurements and communication delays. That is, a new compensation filtering method within the time-varying framework is presented based on the predictive estimation and the innovation measurements. A locally minimum upper bound matrix for the estimation error covariance is obtained by properly designing the distributed filter gain at every sampling step. Furthermore, the performance analysis problem of the prediction-based distributed filtering algorithm is discussed by providing the desirable theoretical derivations. Finally, some comparative simulations are used to show the advantages of the presented prediction-based distributed filtering strategy under delay compensation mechanism.