Haze in natural environments is usually non-homogeneous and irregular， which has a large impact on computer vision tasks. Therefore， this paper proposed the Enhanced-edge-feature Dual-branch Fusion Dehazing Network （EDFDNet）. In order to retain the realism of the image and at the same time effectively improve the visibility after dehazing in the case of severe blurring， the transmission graph fine branch was constructed， which was the premier branch of the network. A U-shaped network hierarchical codec structure that fused the discrete wavelet transform was used to extract multi-scale fine feature information， and a mathematical method for the determination of the enhanced edge information was defined. The feature extraction branch tandemly connected the ResNet residual block and the Transformer combined with dual attention for a parallel feature extraction module， which fused the extracted local and global features. This improved the network's ability to understand and process non-uniform haze images and further restored the visibility of the images. These two branches were joined into the backbone framework of the Generative Adversarial Network （GAN）， and a mathematical method to strengthen the determination of edge information was defined. This formed the defogging network EDFDNet.The results of the experiments show that the average PSNR and SSIM of this method on the outdoor synthetic dataset are improved by 1.256 7 and 0.030 8， respectively， compared with the optimal results of the current mainstream methods.Meanwhile， in the test on the real-world dataset， the PIQE， RI， and VI reach the optimal indexes of 21.471， 0.971 1 and 0.900 3.EDFDNet achieves good results in both realism enhancement and visibility restoration， and is suitable for dehazing real-world non-uniform haze images.