For necessary information sharing or operation control via wire-wireless/mobile network connecting of devices at disaster area in greatest need of attention, an emergency network efficient construction method quickly connecting nodes within specific range using Delaunay triangulation is proposed. The emergency network constructed by proposed method shows the same aggregate network length, but does more excellent performance in term of network construction time the more long max length connectable to adjacent node as compared with the network by naive method. In experiment of 1000 input terminal nodes, 5 max length connectable to adjacent node, our proposed method enhances 89.1% in execution time without network length increase compared to naive method. So our method can go well to many useful applications as shift construction of communication network of adjacent devices, internet of things and efficient routing in the sensor network in continuous improvement of communication capability.