A well-defined cost function is a key issue for image steganography to minimize the embedding distortion. In recent years, deep learning has been introduced into image steganography to automatically learn embedding costs and improve steganographic security. For most existing generative adversarial network (GAN) based cost learning works, the generator usually adopts an encoder–decoder architecture. However, due to repeated encoding and decoding operations, this architecture is prone to information loss, making the generator difficult to well capture fine-grained image features. In this work, we propose a novel GAN-based image steganography work that improves the cost function by learning better embedding probability maps. Specifically, we design an attention mechanism to be integrated into the U-Net architecture, which enables the generator to concentrate on texture-rich regions of input images. Moreover, an extra input stream, namely the enhanced image, is introduced into the generator, improving the generator’s ability to learn structural features from input images. Different skip connections are used for different input streams to facilitate information flow between different layers. Extensive experimental results demonstrate that the proposed approach effectively learns the embedding probability maps and achieves superior security against various steganalysis attacks.