This paper proposes a centralized MTT method based on a state-of-the-art multi-sensor labeled multi-Bernoulli (LMB) filter in underwater multi-static networks with autonomous underwater vehicles (AUVs). The LMB filter can accurately extract the number of targets and trajectories from measurements affected by noise, missed detections, false alarms and port–starboard ambiguity. However, its complexity increases as the number of sensors increases. In addition, due to the time-varying underwater environment, AUV detection probabilities are time-varying, and their mismatches often lead to poor MTT performance. Consequently, we detail a robust multi-sensor LMB filter that estimates detection probabilities and multi-target states simultaneously in real time. Moreover, we derive an effective approximate form of the multi-sensor LMB filter using Kullback–Leibler divergence and develop an efficient belief propagation (BP) implementation of the multi-sensor LMB filter. Our method scales linearly with the number of AUVs, providing good scalability and low computational complexity. The proposed method demonstrates superior performance in underwater multi-AUV network MTT simulations.