Ordinary underwater nodes may move with water current or other activities, while autonomous underwater vehicles (AUVs) move autonomously in water, all these result in the highly dynamic network topology, which bring about great challenge for the routing in underwater sensor networks (UWSNs). Consequently, energy-efficient routing protocols for UWSNs with mobile nodes become the focus of research. To cope with the problem of node mobility and energy efficiency in UWSNs, we propose a layering routing protocol based on node mobility prediction (LR-NMP) for UWSNs in this article. First, a node movement prediction model based on the improved GM(1,1) is proposed, and a rule of node mobility prediction is presented. With the LR-NMP routing protocol, only the neighbor nodes with less level can become the candidate next hop nodes. For each candidate node, a mobility prediction index (MPI) is computed according to the proposed movement prediction model. Furthermore, a path selection factor (PSF) for the candidate node is determined based on the MPI and the path forwarding cost of the candidate node, and the candidate node with the smallest PSF is selected as the best next hop node. To decrease the end-to-end delay (EED), the interaction of control packets is limited by the changing degree of topology. Simulation results show that the LR-NMP protocol can work well in UWSNs with moving nodes at different speeds. In mobility scenarios, the packet delivery rate (PDR) increases by 10%–20%, the EED decreases by about -1 to -7 s, and the average energy consumption reduces by 0.1–5 J.