In Wireless Sensor Network (WSN), the clustering algorithm was developed to reduce the total energy consumption which determines the lifetime of the whole network. As a result, a number of recently-designed energy-efficient routing algorithms stated that clustering approach has an important issue for organizing a network into a connected hierarchy and increasing the network lifetime. This paper proposes a new algorithm to improve the performance of Low Energy Adaptive Clustering Centralized (LEACH-C) by improving the criterion for electing a cluster-head and the determination of optimal number of cluster-heads. Firstly, the optimal number of cluster-heads is based on the density of the covering. The sensor nodes are deployed randomly on the plane area of the sensing field covered by the communication range of the node. Secondly, nodes having the highest remaining energy and the lowest energy variance consumption becomes cluster-heads. The variance parameter keeps energy consumption dispersion, if the considered node is elected as cluster-head. This dispersion highly depends on the relative positioning of the node to the base station. This is useful for predicting node status when elected as cluster-head in the current round in order to balance the network energy. The simulation and analytical results of the proposed algorithm outperform the existing protocols in terms of lifetime of the network.