Oceanic mesoscale eddies greatly influence energy and matter transport and acoustic propagation. However, the traditional detection method for oceanic mesoscale eddies relies too much on the threshold value and has significant subjectivity. The existing machine learning methods are not mature or purposeful enough, as their train set lacks authority. In view of the above problems, this paper constructs a mesoscale eddy automatic identification and positioning network—OEDNet—based on an object detection network. Firstly, 2D image processing technology is used to enhance the data of a small number of accurate eddy samples annotated by marine experts to generate the train set. Then, the object detection model with a deep residual network, and a feature pyramid network as the main structure, is designed and optimized for small samples and complex regions in the mesoscale eddies of the ocean. Experimental results show that the model achieves better recognition compared to the traditional detection method and exhibits a good generalization ability in different sea areas.