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Localization is one of the basic prerequisites of sensors in various applications of wireless sensor networks. A beacon is a special sensor with geographical knowledge and which can be employed to help localize general sensors. A mobile beacon is treated as a replacement for many static beacons since it is movable and flexible and often powerful. The path of a mobile beacon will determine the rate of coverage and accuracy of position determination that it supports. Whereas a static path is planned before any localization action, a dynamic path is determined in real-time based on the demands of initially unknown sensors and hence can be more efficient than a static path. In this paper, we proposed a method of localization employed a mobile beacon whose path will be selected according to the real-time information of unknown sensors. The method is designed to be both “thrifty” in both energy consumption and economical cost, and lightweight in terms of computation load. Simulation results show that the method is lightweight but effective and efficient.