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Addressing plays an important role in traditional networks but incurs much overhead for resource-constrained wireless sensor networks (WSNs).Therefore, address-free sensor network has been proposed by researchers. However, current data delivery schemes are mainly proposed for address-based sensor networks and can't be directly applied to the new architecture. In this paper, we propose an efficient data delivery scheme (EDDS) for address-free wireless sensor networks, in which data source nodes randomly select a probabilistically unique identifier for each data flow instead of statically assigned node addresses. The packet forwarding mechanism in EDDS combines the tasks of routing and MAC layer via cross-layer design, which simplifies the protocol stack while maintaining the necessary functionality. EDDS can also efficiently handle the changes of the network, such as node death and replenishment. Through analysis and simulations, we evaluate the performance of the proposed scheme and compare it with some previous work.