Localization is one of the fundamental problems in many wireless sensor networks applications, but most of them require the node to equip special range-determining or angle-determining hardware in order to obtain the position related information. In this paper, we propose a concentric beacons localization algorithm which is a range-free approach. Four anchors are set in the four corners of the square target region, and emit localizing beacons at different power levels, with the information of their position and the estimated range of the beacon. The nodes in this region receive these beacons and compute their positions correspondingly. In region of different scale, we propose two alternative schemes. The one for small scale has lower calculation complexity, and the other has better stability on large scale applications. Simulation results show the estimation error is less than 0.4 times the beacon interval.