X-ray computed tomography (X-ray CT) has been widely used in the earth sciences, as it is non-destructive method for providing us the three-dimensional structures of rocks and sediments. Rock samples essentially possess various-scale structures, including millimeters to centimeter scales of layering and veins to micron-meter-scale mineral grains and porosities. As the limitations of the X-ray CT scanner, sample size and scanning time, it is not easy to extract information on multi-scale structures, even when hundreds meter scale core samples were obtained during drilling projects. As the first step to overcome such barriers on scale-resolution problems, we applied the super-resolution technique by sparse representation and dictionary-learning to X-ray CT images of rock core sample. By applications to serpentinized peridotite, which records the multi-stage water-rock interactions, we reveal that both grain-shapes, veins and background heterogeneities of high-resolution images can be reconstructed through super-resolution. We also show that the potential effectiveness of sparse super-resolution for feature extraction of complicated rock textures.