This article addresses a problem of seabed terrain following control (STFC) for an underwater vehicle-manipulator system (UVMS). The motivation is to perform a visual search of marine products closely to seabed in unknown environment. In terms of this issue, we propose a novel and robust STFC framework for our UVMS to maintain an appropriate height to seabed. A nonlinear model predictive control (NMPC) method is formulated to solve the STFC problem. To relieve online computational burden and system noisy influence, Ohtsuka's continuation/generalized minimal residual (C/GMRES) algorithm incorporated with a tracking differentiator (TD) is investigated. In order to improve the following accuracy, the system state prediction part of the NMPC and a long short-term memory (LSTM) network are elaborated to predict future seabed terrain using a depth gauge and an altimeter, respectively. Finally, the three different physical scenarios for STFC problem are established using ROS to demonstrate the robustness and efficiency of the proposed algorithm.