Marine oil spills due to ship collisions or operational errors have caused tremendous damage to the marine environment. In order to better monitor the marine environment on a daily basis and reduce the damage and harm caused by oil pollution, we use marine image information acquired by synthetic aperture radar (SAR) and combine it with image segmentation techniques in deep learning to monitor oil spills. However, it is a significant challenge to accurately distinguish oil spill areas in original SAR images, which are characterized by high noise, blurred boundaries, and uneven intensity. Hence, we propose a dual attention encoding network (DAENet) using an encoder–decoder U-shaped architecture for identifying oil spill areas. In the encoding phase, we use the dual attention module to adaptively integrate local features with their global dependencies, thus improving the fusion feature maps of different scales. Moreover, a gradient profile (GP) loss function is used to improve the recognition accuracy of the oil spill areas’ boundary lines in the DAENet. We used the Deep-SAR oil spill (SOS) dataset with manual annotation for training, testing, and evaluation of the network, and we established a dataset containing original data from GaoFen-3 for network testing and performance evaluation. The results show that DAENet has the highest mIoU of 86.1% and the highest F1-score of 90.2% in the SOS dataset, and it has the highest mIoU of 92.3% and the highest F1-score of 95.1% in the GaoFen-3 dataset. The method proposed in this paper not only improves the detection and identification accuracy of the original SOS dataset, but also provides a more feasible and effective method for marine oil spill monitoring.