Abstract: To address the multi-source time-varying disturbance problems, such as target motion uncertainty, unknown environmental disturbances, and model parameter perturbations, faced by Autonomous Underwater Vehicles (AUVs) during dynamic target tracking, as well as the characteristic of limited AUV computing resources, this paper proposes a robust Model Predictive Control (MPC) strategy for AUV target tracking that integrates time-varying disturbance estimation, prediction, and compensation. First, a relative motion Extended State Observer (ESO) model is constructed from the perspective of a sub-AUV to lump multi-source disturbances into a total disturbance and achieve real-time estimation; Second, a receding horizon disturbance predictor model is designed. Based on the historical disturbance sequence data estimated by the ESO, the matrix pencil method is used to extract the initial values of the dominant modes, and the least squares nonlinear optimization is employed to estimate the modal parameters, balancing the solution accuracy and efficiency of the model, and the disturbance sequence is fitted into an explicit function of time to achieve short-term prediction of time-varying disturbances; Finally, based on the system model embedded with disturbance prediction information, a Model Predictive Controller is designed. The feedforward compensation of future disturbances is explicitly incorporated into the optimization problem, and the TinyMPC solving framework suitable for computationally constrained applications is adopted and improved, thereby forming a disturbance-rejection MPC framework with multi-step disturbance feedforward compensation. Simulation experiments show that, compared with existing single-step or multi-step fixed disturbance value compensation methods such as ESO-MPC, the proposed method can significantly improve control accuracy when tracking time-varying targets; Tank experiments further verify the adaptability and engineering feasibility of the algorithm for tracking moving targets with different periods.