Accurate detection of sea ice leads is essential for safe navigation in polar regions. In this paper, a shape-aware (SA) network, SA-DeepLabv3+, is proposed for automatic lead detection from synthetic aperture radar (SAR) images. Considering the fact that training data are limited in the task of lead detection, we construct a dataset fusing dual-polarized (HH, HV) SAR images from the C-band Sentinel-1 satellite. Taking the DeepLabv3+ as the baseline network, we introduce a shape-aware module (SAM) to combine multi-scale semantic features and shape information and, therefore, better capture the shape characteristics of leads. A squeeze-and-excitation channel-position attention module (SECPAM) is designed to enhance lead feature extraction. Segmentation loss generated by the segmentation network and shape loss generated by the shape-aware stream are combined to optimize the network during training. Postprocessing is performed to filter out segmentation errors based on the aspect ratio of leads. Experimental results show that the proposed method outperforms the existing benchmarking deep learning methods, reaching 96.82% for overall accuracy, 93.01% for F1-score, and 91.48% for mIoU. It is also found that the fusion of dual-polarimetric SAR channels as the input could effectively improve the accuracy of sea ice lead detection.