For ocean exploration high speed data transmission is the emergent requirement. Acoustic sensor networks are available to support large distances but with lower data rates and also consume maximum energy. Optical networks can be used to support high speed data transmission but it cannot be used for larger distances. Underwater Wireless Sensor Networks (UWSN) suffer from large propagation delay, high bit error rates, limited bandwidth, uncontrolled node mobility, water current and limited resources. Hence there is an evolving requirement for design and use of an efficient routing protocol. In the proposed research, design of an Optimal Distributed Energy Efficient Hybrid Optical -Acoustic Cluster Based Routing Protocol (EEHCRP) to minimize the energy consumption in Underwater Wireless Sensor Networks is considered. To overcome these problems we propose an Energy Efficient Hybrid Optical-Acoustic Cluster Based Routing Protocol for Underwater Wireless Sensor Network (EEHCRP).In this research work we study various network parameters like network throughput, network life time, average energy consumption, end to end delay and data delivery ratio for mobile nodes ranging from 50 to 500. It is observed that there is an average increase of 0.9% network throughput in the proposed EEHRCP protocol compared to CBE2R protocol. The network life time is increased to 51.2 seconds with a decrease in 0.93% of energy consumption and 0.48 % decrease in end to end delay in the proposed protocol EEHRCP compared to CBE2R protocol. There is an increase in 0.95% of data delivery ratio using the proposed EEHRCP protocol compared to E-CBCCP protocol.