This paper considers the state estimation problem for discrete-time systems in a network environment. Specifically, the network-induced delay from the sensor node to the estimator node is modeled as a finite set of delays with corresponding occurrence probabilities. The design of switched filters is proposed. The switching is performed according to the detected time delay. The occurrence probability of the delay is incorporated into the filter design, which can improve the filtering performance. Simulation studies and comparisons illustrate the effectiveness and the improvement of the proposed design method.