Underwater dynamic target tracking technology has a wide application prospect in marine resource exploration, underwater engineering operations, naval battlefield monitoring, and underwater precision guidance. Aiming at the underwater dynamic target tracking problem, an autonomous underwater vehicle tracking control method based on trajectory prediction is studied. First, a deep learning-based target detection algorithm is developed. For the image collected by the multibeam forward-looking sonar image, this algorithm uses the YOLO v3 network to determine the target in a sonar image and obtain the position of the target. Then, a time profit Elman neural network (TPENN) is constructed to predict the trajectory information of the dynamic target. Compared with an ordinary Elman neural network, its accuracy of dynamic target prediction is increased. Finally, underwater tracking of the dynamic target is realized using the model predictive controller (MPC), and the tracking result is stable and reliable. Through simulations and experiment, the proposed underwater dynamic target tracking control method is demonstrated to be effective and feasible.