In order to further improve the coherence speckle suppression and edge preservation performance of synthetic aperture radar (SAR) images by deep learning methods, a coherence speckle suppression method based on edge-guided dual-branch network was proposed. The method constructed a new speckle suppression network model, which consisted of an edge information extraction block and a dual-branch speckle suppression network. Firstly, a dense cascade strategy was used to build the edge information extraction block to enhance the edge perception capability of the model. Secondly, the channel attention-based residual despeckling network (CARNet), the mixed attention-based enhanced despeckling network (MAENet), and the multi-branch parallel based multi-scale feature fusion block (MPMFFB) were used to form a dual-branch speckle suppression network, so as to better preserve edge details while suppressing coherence speckles. The experimental results show that the proposed method has better coherence speckle suppression and edge preservation performance compared with recent state-of-the-art methods such as SAR-Transformer and HTNet. For the simulated SAR images, the peak signal to noise ratio, structural similarity index measure, and edge preserve index are improved by 0.96 dB, 2.60%, and 0.60% on average, respectively. For the real SAR images, the equivalent number of looks is improved by more than 14.12%, and the edge preserve index is improved by 4.52% on average.