This paper proposes a distributed energy-efficient data gathering and aggregation protocol, in which a node, according to its residual energy and the strength of the signal received from its neighboring nodes, independently makes its decision to compete for becoming a cluster head. In addition, assume that the inter-cluster communication data in a multi-hop manner is sent to the designated node, it then sends the gathered data by the whole network to the base station. DEEG also proposes a simple approach to solve the cluster coverage problem. With the increase in node density, this approach produces a linear sensor network lifetime in the number of nodes. Experimental results have shown that compared with another two data gathering and aggregation protocols--- leach and PEGASIS, the DEEG algorithm, in the best case, can lead to the increase of sensor network lifetime by 1800% and 300% respectively. Moreover, since all the nodes in the sensor network die in the last 40 rounds (the last node dies) in DEEG protocol, the reliability of the sensing information in DEEG is higher than that in LEACH and PEGASIS.