Aiming at the inefficiency of the relay selection of data gathering protocol for multi-hop wireless sensor networks（WSN）

an energy efficient relay node fast selection（EERNFS） algorithm was proposed.In EERNFS

time-sharing channel was adopted to maintain time synchronization of WSN and periodically update the information of the neighbor network node.The network nodes could be activated synchronously in any network listening/sleeping cycle according to a certain probability

thus the real-time consistency and the stability of the nodes’ connectivity degree in WSN were guaranteed.Based on the geographic priority

the value of the nodes and the distribution estimation of the route-link quality

the relay node was selected through the competition method and the competing between the candidate relay nodes was reduced through gradually multiplying time window method.Theoretical analysis and simulation results show that EERNFS outperforms FFS（forwarder fast selection） and GeRaF in terms of energy efficiency

delay of data delivery

and data delivery rate so that the network lifetime is greatly prolonged.