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In the field of structural health monitoring based on wireless sensor networks, usually using clustering routing algorithm, the structural damage identification is achieved by two structural features, natural frequencies and mode shapes. This kind of routing algorithm in specific applications needs to meet certain constraints, such as the single-hop-communication between cluster head node and each node in cluster, the overlap between different clusters and so on. To meet with the special constraints for clustering routing algorithm in structural health monitoring, this paper proposed a new method based on minimal connected cover set, which is called Enhanced Greedy Algorithm based D(v) (DEGA) routing algorithm. The DEGA method can achieve the minimum connected cover by node's own degree D(v), and can meet the structural health monitoring routing constraints. The simulation experiments on NS2 show that, DEGA algorithm to get minimum cover set performance is superior to the traditional greedy algorithm. Compared with the classic HEED clustering routing algorithm, DEGA algorithm has better energy resistance, and can be maintain a longer network lifetime.