In this paper,a hierarchical clustering protocol for long-lived sensor network is proposed. EADEEG(an energy-aware data gathering protocol for wireless sensor networks) achieves a good performance in terms of lifetime by minimizing energy consumption for communications and balancing the energy load among all nodes. EADEEG adopts a new clustering parameter for cluster head election,which can better handle the hetergenous energy capacities. Furthermore,it also adopts a simple but efficient approach,namely intra-cluster coverage to cope with the fractional area coverage problem. Through turning off redundant nodes,while the remaining nodes stay active to provide continuous service,the network lifetime can be significantly prolonged. Experimental results have shown that EADEEG can satisfy the desired coverage fraction and outperform LEACH(low energy adaptive clustering hierarchy) ,PEGASIS(power-efficient gathering in sensor information systems) and DEEG(distributed energy-efficient data gathering and aggregation protocol) in terms of network lifetime.