High-resolution(HR) magnetic resonance images (MRI) can improve the accuracy of disease diagnosis, but it is very difficult to obtain high-resolution MRI. Image super-resolution (SR) technology based on deep learning can effectively improve image resolution. In recent years, the generative adversarial networks (GANs) have provided new ideas for 3D-MRI SR reconstruction. Compared with the traditional SR algorithm based on deep convolutional neural network (DCNN), the GANs network targets the human visual mechanism and introduces a discriminant function to make the reconstructed 3D-MRI closer to the real image. We introduced the enhanced super-resolution generative adversarial network (ESRGAN) to perform SR reconstruction of 3D-MRI, and used the cross-layer self-similarity of 3D-MRI to reduce the dimensionality of the reconstruction task to 2D. On the basis of ensuring the reconstruction effect, the proposed method can reduce network training time and memory requirements. Compared with other traditional algorithms and DCNN-based techniques, experimental results show that our proposed method can further improve the visual quality of SR 3D-MRI.