Digital core reconstruction can quantitatively characterize the interior microstructure of porous media and revealing variations in the petrophysical properties of rocks, which can be classified into physical experimental methods and numerical reconstruction methods. Numerical reconstruction methods utilize the information contained in 2D or 3D images to reconstruct 3D digital cores, which is relatively inexpensive and more efficient, but traditional numerical methods usually cannot reuse extracted statistical information from previous reconstruction process and may generate unsatisfying results. Nowadays, the development of deep learning has opened a door to the high-quality reconstruction of digital cores. Generative adversarial networks (GANs), viewed as an important branch of deep learning, have been used for the 3D digital core reconstruction. GANs have a strong feature extraction capability and can generate fake images that closely resemble the real ones. Nevertheless, due to the complex structure of 3D core images, especially those with high anisotropy, GANs and their variants still have difficulties in generating satisfying pore structure. To address the above issues, we propose a variant of GANs called 3D fast generative adversarial network (3D-FGAN) to rapidly generate high-quality 3D digital core images. Several channel attention modules called skip-layer excitation blocks are added to the generator of 3D-FGAN, enhancing the utilization of important features. Auto-encoders are employed to optimize the discriminator of 3D-FGAN, which makes the discriminator more comprehensively extract the features of input images and thus better guides the generator. Through the evaluation metrics of pore space distribution (e.g., isolated pore space and connected pore space, pore diameters and throat diameters), multiple-point connectivity, absolute permeability and diversity test, the quality of 3D-FGAN can be proved. Meanwhile, in the reconstruction of anisotropic shales with evident fractures, 3D-FGAN can quickly produce higher-quality images compared with some other numerical reconstruction methods.