In order to analyze fish behavior, real-time underwater fish monitoring is essential. This work presents an underwater multi-target tracking algorithm for aquaculture monitoring, utilizing deep learning techniques. Underwater images are acquired using an underwater robot, and the images are defogged using the multi-scale Retinex algorithm based on HSV space. To enhance object detection performance, GhostNetv2 was integrated into the You Only Look Once version 5 (YOLOv5) object detection algorithm, supplemented by the addition of the Coordinate Attention (CA) module, resulting in the development of GN-YOLOv5. For the tracking algorithm, the more accurate Generalized Intersection over Union (GIoU) method was incorporated into the StrongSORT tracking algorithm. Moreover, to achieve more precise target tracking, a fish re-identification model was established. The proposed algorithms were evaluated through experiments conducted on various datasets, including VOC 2012, MOT16, and self-built datasets. The results demonstrate notable improvements: the GN-YOLOv5 model showed a 32.91% reduction in parameters and a 3.22% increase in precision. Furthermore, the enhanced StrongSORT algorithm exhibited a 3.84% increase in MOTA, a 28.00% reduction in IDS, and a speed boost of 7 FPS, leading to stable and accurate multi-target fish tracking.