The trajectory tracking of Autonomous Underwater Vehicles (AUV) is an important research topic. However, in the traditional research into AUV trajectory tracking control, the AUV often follows human-set trajectories without obstacles, and trajectory planning and tracking are separated. Focusing on this separation, a trajectory re-planning controller based on Model Predictive Control (MPC) is designed and added into the trajectory tracking controller to form a new control system. Firstly, an obstacle avoidance function is set up for the design of an MPC trajectory re-planning controller, so that the re-planned trajectory produced by the re-planning controller can avoid obstacles. Then, the tracking controller in the MPC receives the re-planned trajectory and obtains the optimal tracking control law after calculating the object function with a Sequential Quadratic Programming (SQP) optimisation algorithm. Lastly, in a backstepping algorithm, the speed jump can be sharp while the MPC tracking controller can solve the speed jump problem. Simulation results of different obstacles and trajectories demonstrate the efficiency of the proposed MPC trajectory re-planning tracking control algorithm for AUVs.