Post-stack seismic profiles are images reflecting geological structures which provide a critical foundation for understanding the distribution of oil and gas resources. However, due to the limitations of seismic acquisition equipment and data collecting geometry, the post-stack profiles suffer from low resolution and strong noise issues, which severely affects subsequent seismic interpretation. To better enhance the spatial resolution and signal-to-noise ratio of post-seismic profiles, a multi-scale attention encoder–decoder network based on generative adversarial network is proposed. This method improves the resolution of post-stack profiles and effectively suppresses noises and recovers weak signals as well. A multi-scale residual module is proposed to extract geological features under different receptive fields. At the same time, an attention module is designed to further guide the network to focus on important feature information. Additionally, to better recover the global and local information of post-stack profiles, an adversarial network based on a Markov discriminator is proposed. Finally, by introducing an edge information preservation loss function, the conventional loss function of the Generative Adversarial Network is improved, which enables better recovery of the edge information of the original post-stack profiles. Experimental results on simulated and field post-stack profiles demonstrate that the proposed multi-scale attention encoder–decoder network based on generative adversarial network method outperforms two advanced convolutional neural network-based methods in noise suppression and weak signal recovery. Furthermore, the profiles reconstructed by the multi-scale attention encoder–decoder network based on generative adversarial network method preserve more geological structures.