Stochastic reconstruction of digital core images is a vital part of digital core physics analysis, aiming to generate representative microstructure samples for sampling and uncertainty quantification analysis. This paper proposes a novel reconstruction method of the digital core of shale based on generative adversarial networks (GANs) with powerful capabilities of the generation of samples. GANs are a series of unsupervised generative artificial intelligence models that take the noise vector as an input. In this paper, the GANs with a generative and a discriminative network are created respectively, and the shale image with 45 nm/pixel preprocessed by the three-value-segmentation method is used as training samples. The generative network is used to learn the distribution of real training samples, and the discriminative network is used to distinguish real samples from synthetic ones. Finally, realistic digital core samples of shale are successfully reconstructed through the adversarial training process. We used the Fréchet inception distance (FID) and Kernel inception distance (KID) to evaluate the ability of GANs to generate real digital core samples of shale. The comparison of the morphological characteristics between them, such as the ratio of organic matter and specific surface area of organic matter, indicates that real and reconstructed samples are highly close. The results show that deep convolutional generative adversarial networks with full convolution properties can reconstruct digital core samples of shale effectively. Therefore, compared with the classical methods of reconstruction, the new reconstruction method is more promising.