Marine acoustic passive target tracking has received much attention from researchers as an important part of ocean exploration. This issue becomes challenging in complex marine environments when the target motion model changes abruptly. The primary objective of underwater passive target tracking is to acquire the bearing parameters of the target from the observation station. In this paper, we apply Long Short-Term Memory (LSTM) neural network and dual observation stations system to the problem of underwater target bearings-only trajectory tracking. Results of computer simulation prove the stability of the proposed algorithm in the problem of bearings-only target tracking when only angles are measured, and effectively reduce the root-mean-square error. Therefore, this study provides a new technical solution for underwater bearings-only maneuvering target tracking.