In the process of landing unmanned aerial vehicles (UAVs) on an unmanned surface vehicle (USV), a manipulator can be applied to help the UAV land safely and accurately. However, it is a challenge to control the manipulator on a disturbed USV due to joint velocity constraints and bandwidth limitations. To solve this problem, a predictive control framework is proposed in this paper. We leverage a first-order delay system to describe the kinematics of each joint, and control joint velocities by the model predictive controller (MPC). To generate references for MPC, the motion of the floating base needs to be predicted. We apply the recent approach for motion prediction based on the wavelet network (WN) and modify the network to get smooth trajectories. The accuracy of the modified wavelet network (MWN) for motion prediction is tested on four-hour motion data from the real ocean environment and the smoothness of the generated trajectories is also evaluated. Simulations and experiments are implemented to verify the proposed method, the results show that the average control accuracies are improved by more than 30% and 50% in position and rotation compared with the traditional inverse kinematics (IK) controller for 1 Hz base fluctuation.