Wireless sensor networks are embedded with distributed set of sensor nodes that are cooperatively monitor physical or environmental conditions, and send their information to a “sink” node over multi hop wireless communication links.  The sensor nodes battery energy depletion will significantly affect the network lifetime of a WSN. Most researchers have aimed to design energy-aware routing protocol to minimize the usage of the battery energy to prolong network lifetimes. This paper proposes a sink relocation approach for efficient utilization of sensor’s battery energy called Energy Efficient Sink Relocation Scheme (E-SRS) which considers regulation of transmission coverage range depend on the residual energy of a sensor node.  The EE-SRS proposed in this paper discusses the algorithm to find the optimal place for relocating the sink, and “when and where to relocate the sink”. The EE-SRS algorithm is developed and simulated using network simulator. The performance analysis has also been done in terms of the network lifetime, throughput and packet delay.