Developing an energy efficient routing protocol for underwater wireless sensor networks (UWSNs) is a challenging task due to long propagation delay, low bandwidth, high error probability, and most importantly limited energy. Unlike ter-restrial sensor networks, UWSN environment is harsh. Nodes are provided with limited energy. The replacement or charging of batteries is not an easy task. By minimizing number of transmissions and considering some time critical applications. We have proposed an enhanced energy efficient depth based routing protocol, EEEDBR, for UWSNs. EEEDBR, selects a forwarding node based on high residual energy, least depth from the sink. In EEEDBR network lifetime is increased by deploying idle nodes in the medium depth region. As, sensor nodes gets die earlier in low or medium depth region due to the additional relaying of data packets. Moreover, In our proposed scheme nodes can vary their transmission range up to a certain limit in order to find a suitable forwarding node.