Although numerous works have been done on optimising energy usage of sensors existing in Underwater Wireless Sensor Networks UWSNs, no work has been done on jointly considering the mutual interconnections among paths of multi-source nodes under the given network topology and acoustic channel conditions. In this work, we consider the problem of data transmission from multiple source nodes to the sink node. The main contributions of this work are: a node significance is defined based on the distance and source node statuses; b given a number of source nodes, we formulate the problem of energy-efficient multiple paths, and develop a polynomial-time algorithm for deriving the optimal paths; c to refine the feasible number of source nodes, the upper and lower bounds are derived based on the network topology and acoustic channel conditions. Extensive simulation results show that our proposed scheme can achieve significant performance enhancement over the existing ones.