In this paper, we propose a novel range-free localization algorithm tailored for mobile wireless sensor networks (MWSN)s. In contrast to the most existing range- free algorithms, the nodes mobility is taken into accounts when designing our algorithm. We show that nodes are able to estimate their positions using solely their locally-available information, thereby avoiding any unnecessary overhead and power costs incurred if information exchange between nodes was required. Furthermore, we show that the proposed algorithm outperforms in accuracy the best representative range-free algorithms. In contrast to the latter, it is able to compensate the nodes mobility effects when the nodes' speeds are moderate.