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Wireless sensor networks will become very useful in the near future. The efficient energy consumption in wireless sensor network is a critical issue since the energy in the nodes is constrained resource. In this paper, we present a transmission relay method of communications between BS (Base Station) and CHs (Cluster Heads) for balancing the energy consumption and extending the average lifetime of sensor nodes by the fuzzy logic application. The proposed method is designed based on LEACH protocol. The area deployed by sensor nodes is divided into two groups based on distance from BS to the nodes. RCH (Relay Cluster Head) relays transmissions from CH to BS if the CH is in the area far away from BS in order to reduce the energy consumption. RCH decides whether to relay the transmissions based on the threshold distance value that is obtained as a output of fuzzy logic system. Our simulation result shows that the application of fuzzy logic provides the better balancing of energy depletion and prolonged lifetime of the nodes.