The most significant challenge of underwater optical wireless communication (UOWC) system is to overcome its limited coverage. To expand the achievable communication range, we investigate the performance of the dual-hop UOWC system with simultaneous lightwave information and power transfer (SLIPT). The time splitting (TS) method is adopted for wireless power transfer in the proposed system, where the information and energy are transmitted in different phases. A suitable transmission strategy is designed for the model without additional power supply, which contains three phases, i.e. information transmission, energy transmission, and forwarding process. The expressions of the average bit error rate (BER) at the target node and the energy harvested by the relay node are derived over underwater attenuation channel. Then, the effects of the TS factor and the distances on the system performance are investigated in two sub-problems, which minimize the average BER while satisfying the energy harvesting and transmitting rate constraints. Numerical results indicate the performance improvement by adopting the relay node with SLIPT.