In this paper, the complete process of constructing 3D digital core by full convolutional neural network is described carefully. A large number of sandstone computed tomography (CT) images are used as training input for a fully convolutional neural network model. This model is used to reconstruct the three-dimensional (3D) digital core of Berea sandstone based on a small number of CT images. The Hamming distance together with the Minkowski functions for porosity, average volume specific surface area, average curvature, and connectivity of both the real core and the digital reconstruction are used to evaluate the accuracy of the proposed method. The results show that the reconstruction achieved relative errors of 6.26％, 1.40％, 6.06％, and 4.91％ for the four Minkowski functions and a Hamming distance of 0.04479. This demonstrates that the proposed method can not only reconstruct the physical properties of real sandstone but can also restore the real characteristics of pore distribution in sandstone, is the ability to which is a new way to characterize the internal microstructure of rocks.