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Localization is an essential and important research issue in wireless sensor networks (WSNs). Most localization schemes focus on static sensor networks. However, mobile sensors are required in some applications such that the sensed area can be enlarged. As such, a localization scheme designed for mobile sensor networks is necessary. In this paper, we propose a localization scheme to improve the localization accuracy of previous work. In this proposed scheme, the normal nodes without location information can estimate their own locations by gathering the positions of location-aware nodes (anchor nodes) and the one-hop normal nodes whose locations are estimated from the anchor nodes. In addition, we propose a scheme that predicts the moving direction of sensor nodes to increase localization accuracy. Simulation results show that the localization error in our proposed scheme is lower than the previous schemes in various mobility models and moving speeds.