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Localization algorithm continues to be an important and challenging topic in today's wireless sensor networks (WSNs). In this paper, a novel range-free localization algorithm using expected hop progress (LAEP) to predict the location of any sensor in a WSN is proposed. This algorithm is based on an accurate analysis of hop progress in a WSN with randomly deployed sensors and arbitrary node density. By deriving the expected hop progress from a network model for WSNs in terms of network parameters, the distance between any pair of sensors can be accurately computed. Since the distance estimation is a key issue in localization systems for WSNs, the proposed range-free LAEP achieves better performance and less communication overhead as compared to some existent schemes like DV-Hop and RAW. In addition, we study the effect of anchor placement on the algorithm performance by deriving the corresponding mean position error range. Extensive simulations are performed and the results are observed to be in good agreement with the theoretical analysis.