Because of its benefits in terms of high speed, non-destructiveness, and three-dimensionality, as well as ease of integration with computer simulation, computed tomography (CT) technology is widely applied in reservoir geology research. However, rock imaging is restricted by the device used as there is not a win–win for both the image receptive field and corresponding resolution. Convolutional neural network-based super-resolution reconstruction has become a hot topic in improving the performance of CT images. With the help of a convolution kernel, it can effectively extract characteristics and ignore disturbance information. The dismal truth is that convolutional neural networks still have numerous issues, particularly unclear texture details. To address these challenges, a generative adversarial network (RDCA-SRGAN) was designed to improve rock CT image resolution using the combination of residual learning and a dual-channel attention mechanism. Specifically, our generator employs residual attention to extract additional features; similarly, the discriminator builds on dual-channel attention and residual learning to distinguish generated contextual information and decrease computational consumption. Quantitative and qualitative analyses demonstrate that the proposed model is superior to earlier advanced frameworks and is capable to constructure visually indistinguishable high-frequency details. The quantitative analysis shows our model contributes the highest value of structural similarity, enriching the more detailed texture information. From the qualitative analysis, in enlarged details of the reconstructed images, the edges of the images generated by the RDCA-SRGAN can be shown to be clearer and sharper. Our model not only performs well in subtle coal cracks but also enriches more dissolved carbonate and carbon minerals. The RDCA-SRGAN has substantially enhanced the reconstructed image resolution and our model has great potential to be used in geomorphological study and exploration.