A wireless sensor network has unidirectional links because sensors can have different transmission ranges, sensors have unstable transmission ranges, and a hidden terminal problem exists. In this paper, we introduce a virtual coordinate assignment protocol (ABVCap_Uni) to assign virtual coordinates to nodes that have no geographic information in wireless sensor networks with unidirectional links, and we propose a routing protocol based on the ABVCap_Uni virtual coordinates. Our routing protocol guarantees packet delivery without computation and storage of global topology features in a discrete domain. Using simulation, we evaluate the performance of the proposed routing protocol (ABVCap_Uni routing), the greedy landmark- descent routing protocol (GLDR+VLM routing), and the greedy routing protocol based on physical coordinates (Euclidean routing). The simulations demonstrate that our routing protocol ensures moderate routing path length cost overhead.