This paper is concerned with the design problem of finite-horizon H∞ fault estimator for a class of nonlinear time-varying systems with Round-Robin protocol scheduling. The faults are assumed to occur in a random way governed by a Bernoulli distributed white sequence. The communication between the sensor nodes and fault estimators is implemented via a shared network. In order to prevent the data from collisions, a Round-Robin protocol is utilized to orchestrate the transmission of sensor nodes. By means of the stochastic analysis technique and the completing squares method, a necessary and sufficient condition is established for the existence of fault estimator ensuring that the estimation error dynamics satisfies the prescribed H∞ constraint. The time-varying parameters of fault estimator are obtained by recursively solving a set of coupled backward Riccati difference equations. A simulation example is given to demonstrate the effectiveness of the proposed design scheme of the fault estimator.