Porous media reconstruction is quite significant in the fields of environmental supervision, oil and natural gas engineering, biomedicine and material engineering. The traditional numerical reconstruction methods such as multi-point statistics (MPS) are based on the statistical characteristics of training images (TIs), but the reconstruction quality may be unsatisfactory and the process is time-consuming. Recently, with the rapid development of deep learning, its powerful ability in predicting features has been used to reconstruct porous media. Generative adversarial network (GAN) is one of the generative methods of deep learning, which is derived from the two-person zero-sum game through the confrontation between the generator and discriminator. However, the traditional GAN cannot pay special attention to the effective features in learning, and the degradation problem easily occurs with the increase of layer numbers. Besides, high-resolution (HR) and large FOV (field of view) are usually contradictory for physical imaging equipment. Therefore, in practical experiments, due to the limitations of the resolution of imaging equipment and the sample size, it is difficult to obtain large-scale HR images of porous media physically. At this point, numerical super-resolution (SR) reconstruction seems to be a cost-efficient way. In this paper, residual networks and attention mechanisms are combined with single-image GAN (SinGAN), which can learn the structural characteristics of porous media from a low-resolution (LR) 3D image, and then reconstruct 3D HR or large-scale images of porous media. Comparison to some other numerical methods has proved that our method can reconstruct high-quality HR images with practicability and effectiveness.