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Mobile anchor node is used for localization in Wireless Sensor Networks. It can lower the cost of network and reduce the dependence of localization precision of the algorithm on the density of anchor nodes. However, in the existing algorithm for the localization of mobile anchor node, little research in detail has been done on the path of mobile anchor node and the timing of sending beacon. In this article, a Mobile Anchor Node Localization based on Archimedes Curve is put forth, which avoids the node's receipt of beacon on a line to the utmost extent due to the anchor node moving alone curvilinear path. In addition, the identification of the communication range of mobile anchor node and the time of sending beacon can eliminate the blind zone of beacon coverage in the network, and secure that every node can receive three beacons at least, thus achieving a relatively accurate localization for all nodes in the network. Simulation result shows lower average error of localization and better performance than DV-HOP and the localization algorithm in which anchor node moving alone scan-line.