As an image processing method, underwater image enhancement (UIE) plays an important role in the field of underwater resource detection and engineering research. Currently, the convolutional neural network (CNN)- and Transformer-based methods are the mainstream methods for UIE. However, CNNs usually use pooling to expand the receptive field, which may lead to information loss that is not conducive to feature extraction and analysis. At the same time, edge blurring can easily occur in enhanced images obtained by the existing methods. To address this issue, this paper proposes a framework that combines CNN and Transformer, employs the wavelet transform and inverse wavelet transform for encoding and decoding, and progressively embeds the edge information on the raw image in the encoding process. Specifically, first, features of the raw image and its edge detection image are extracted step by step using the convolution module and the residual dense attention module, respectively, to obtain mixed feature maps of different resolutions. Next, the residual structure Swin Transformer group is used to extract global features. Then, the resulting feature map and the encoder’s hybrid feature map are used for high-resolution feature map reconstruction by the decoder. The experimental results show that the proposed method can achieve an excellent effect in edge information protection and visual reconstruction of images. In addition, the effectiveness of each component of the proposed model is verified by ablation experiments.