Secure mechanisms are widely in Wireless Sensor Networks (WSNs), not only for improving the network energy consumption and lifetime, it also improves the security between the networked Sensor Nodes (SNs). Key management is a fundamental security mechanism which is equipped in WSN. In this paper, a Random Key Predistribution (RKP) scheme is used in Low-Energy Adaptive Clustering Hierarchy (LEACH) based clustered network. LEACH divides the network into a number of clusters and also it elects the optimum Cluster Head (CH) from each cluster. Then RKP scheme provides the common keys to each SN of the network to improve the secrecy of the network. Combination of LEACH and RKP scheme is named as LEACH-RKP-WSN. After performing key distribution, the data packets are sent from the source (anyone of SN) to Base Station (BS). The performance of LEACH-RKP-WSN was compared with Adequate Sparse Secure and Minkowski distance based Location Privacy (ASSMLP). Thus the result shows energy consumption, packet delivery ratio, throughput and delay and it achieves 12.1%, 2.25%, 6.5% and 2.25% better performance than ASSMLP. The lifetime of the network increased by minimizing the energy consumption of the LEACH-RKP-WSN.