This paper deals with the distributed Ή∞ state estimation problem for a class of discrete time-varying nonlinear systems with both stochastic parameters and stochastic nonlinearities. The system measurements are collected through sensor networks with sensors distributed according to a given topology. The purpose of the addressed problem is to design a set of time-varying estimators such that the average estimation performance of the networked sensors is guaranteed over a given finite-horizon. Through available output measurements from not only the individual sensor but also its neighboring sensors, a necessary and sufficient condition is established to achieve the Ή∞ performance constraint. The desired estimator parameters can be obtained by solving coupled backward recursive Riccati difference equations (RDEs). A numerical simulation example is provided to demonstrate the effectiveness and applicability of the proposed estimator design approach.