A novel Maritime Multi-Object Tracking method is proposed, combining a deep learning-based object detector with target association algorithms to achieve robust sea-surface multi-object tracking. Specifically, the Multi-Object Tracking employs You Only Look Once version 7 detector for object detection. In the data association part, a module for onboard camera motion compensation is developed, a maritime dynamic spatial information-based intersection-over-union is presented as a similarity metric, and a progressive refinement cascade matching strategy is designed to enhance the tracker's sea-surface multi-object tracking capabilities. The Jari Maritime Tracking Dataset is utilised to validate the effectiveness performance of the proposed method. Experimental results demonstrate that compared to the earlier process, the proposed method exhibits a significant enhancement in multiple object tracking accuracy, with an increase of 27.8% and an achieved score of 81.3. In particular, it reduces the number of identifications switching and missed targets, achieving holistically preferable performance. Meanwhile, the speed of the proposed Multi-Object Tracking fulfils the engineering application requirements for an autonomous ship navigation system.