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Precise polyp segmentation is vital for the early diagnosis and prevention of colorectal cancer (CRC) in clinical practice. However, due to scale variation and blurry polyp boundaries, it is still a challenging task to achieve satisfactory segmentation performance with different scales and shapes. In this study, we present a novel Edge-aware Feature Aggregation Network (EFA-Net) for polyp segmentation, which can fully make use of cross-level and multi-scale features to enhance the performance of polyp segmentation. Specifically, we first present an Edge-aware Guidance Module (EGM) to combine the low-level features with the high-level features to learn an edge-enhanced feature, which is incorporated into each decoder unit using a layer-by-layer strategy. Besides, a Scale-aware Convolution Module (SCM) is proposed to learn scale-aware features by using dilated convolutions with different ratios, in order to effectively deal with scale variation. Further, a Cross-level Fusion Module (CFM) is proposed to effectively integrate the cross-level features, which can exploit the local and global contextual information. Finally, the outputs of CFMs are adaptively weighted by using the learned edge-aware feature, which are then used to produce multiple side-out segmentation maps. Experimental results on five widely adopted colonoscopy datasets show that our EFA-Net outperforms state-of-the-art polyp segmentation methods in terms of generalization and effectiveness.