Accurate skin lesion segmentation in dermoscopic images is crucial to the early diagnosis of skin cancers. However, it remains a challenging task due to fuzzy lesion boundaries, irregular lesion shapes, and the existence of various interference factors. In this paper, a novel Attention Synergy Network (AS-Net) is developed to enhance the discriminative ability for skin lesion segmentation by combining both spatial and channel attention mechanisms. The spatial attention path captures lesion-related features in the spatial dimension while the channel attention path selectively emphasizes discriminative features in the channel dimension. The synergy module is designed to optimally integrate both spatial and channel information, and a weighted binary cross-entropy loss function is introduced to emphasize the foreground lesion region. Comprehensive experiments indicate that our proposed model achieves the state-of-the-art performance with the highest overall score in the ISIC2017 challenge, and outperforms several popular deep neural networks on both ISIC2018 and PH2 datasets.