In this paper, we are devoted to investigate the consensus-based distributed state estimation problems for a class of sensor networks within the unscented Kalman filter (UKF) framework. The communication status among sensors is represented by a connected undirected graph. Moreover, a weighted average consensus-based UKF algorithm is developed for the purpose of estimating the true state of interest, and its estimation error is bounded in mean square which has been proven in the following section. Finally, the effectiveness of the proposed consensus-based UKF algorithm is validated through a simulation example.