Exploration of underwater resources, oceanographic data collection, tactical surveillance and natural disaster prevention are some of the areas of Underwater Wireless Sensor Network(UWSN) applications. UWSN is different from traditional wireless sensor network. The later uses radio waves for communication between sensors while the former uses acoustic waves for data transmission. Communication through UWSN is more challenging because of the many challenges associated with acoustic channels such as low bandwidth, high transmission delay, usual path loss and intermittent connectivity. In UWSN, some algorithms were introduced to enhance the lifetime of networks, by using a smaller battery and other for critical data transmission. However, data packets flooding, path loss and low network lifetime are few challenges with immediate attention. This study proposes a novel routing scheme referred to as the energy-efficient multipath routing (E2MR) for UWSN, which is basically designed for long-term monitoring with higher energy efficiency and delivery ratio. The E2MR establishes a priority table, and the forward nodes are selected based on that priority table. Different experiments are carried out by simulating E2MR and compared with Depth-Based Routing (DBR), EEDBR and H2-DAB with respect to the number of live nodes, end-to-end delay, packet delivery ratio and total energy consumption.