Distributed filter in networks mainly involves two stages, local estimation by private observation and information fusion with neighbor nodes based on the underlying topology. Since Bayesian game is a powerful tool to analyze the interaction equilibrium of multi-player with incomplete information in networks, we combine the recursive LMMSE filter with network game of quadratic utilities under the Bayesian filtering framework. In our algorithm, the nodes update their local beliefs on the unknown state by private observations and historical actions from neighbors in network. The proposed framework is not only applicable to distributed filter in networks, but also can be extended to more general signal processing and decision making in networks.