Abstract: In Wireless Sensor Networks（WSNs），energy hole problem is a key factor of affecting the lifetime of networks.In a circular multi-hop sensor network（modeled as concentric coronas），the optimal transmission ranges of all coronas can effectively improve system lifetime.We propose an approximate greedy algorithm for searching trees with maximal lifetime，ASGT（Algorithm for Searching Good Trees）.In ASGT the paper use graph scheme to analyzes the problem，and transform it to a problem of generating optimal tree from original graph.ASGT can not only reduce the searching complexity but also get results approximated to the optimal solution.Furthermore，the simulation results indicate that the lifetime got from ASGT approximates to the lifetime from optimal list.Compared with algorithm in other literatures，ASGT can prolong more than 2 times of system lifetime.