Underwater object detection is a key technology in the development of intelligent underwater vehicles. Object detection faces unique challenges in underwater applications: blurry underwater images; small and dense targets; and limited computational capacity available on the deployed platforms. To improve the performance of underwater object detection, we proposed a new object detection approach that combines a new detection neural network called TC-YOLO, an image enhancement technique using an adaptive histogram equalization algorithm, and the optimal transport scheme for label assignment. The proposed TC-YOLO network was developed based on YOLOv5s. Transformer self-attention and coordinate attention were adopted in the backbone and neck of the new network, respectively, to enhance feature extraction for underwater objects. The application of optimal transport label assignment enables a significant reduction in the number of fuzzy boxes and improves the utilization of training data. Our tests using the RUIE2020 dataset and ablation experiments demonstrate that the proposed approach performs better than the original YOLOv5s and other similar networks for underwater object detection tasks; moreover, the size and computational cost of the proposed model remain small for underwater mobile applications.