The X-ray micro-Computed Tomography (μ-CT) is the primary tool for digital rock imaging, which provides the foundation for numerically studying petrophysical properties of reservoir rocks at the pore scale. However, the finite resolution of μ-CT imaging cannot capture the micro-porosity at the sub-micrometer scale in carbonate rocks. The tradeoff between the resolution and field of view (FOV) is a persisting challenge in the industry. The machine-learning-based single-image super-resolution techniques has rapidly developed in the past few years. It is becoming a promising approach to "super-resolve" low-resolution carbonate rock images. In this study, we present a fast super-resolution generative adversarial network to enhance the image resolution of carbonate rocks. A pre-trained VGG network is implemented to extract important high-level features, from which the perceptual similarity is evaluated between the generated and ground-truth images. The novelty of this study is two-fold. First, the generator is significantly simplified with a fast super-resolution convolutional neural network. On the other hand, the spatial and channel squeeze-and excitation block is applied to recalibrate nonlinear feature mapping so that the quality of super-resolved images is promising even with much fewer residual blocks. To quantify the quality of the super-resolution images, we compare difference maps between the generated and ground-truth images. Numerical results indicate that the proposed network shows excellent potential in enhancing the resolution of heterogeneous carbonate rocks. In particular, the pixel errors are minor, and the super-resolution images exhibit clear and sharp edges and dissolved mineral texture. This study provides a novel machine-learning-based method using a simple generative adversarial network with squeeze and excitation blocks to super-resolve μ-CT images of carbonate rocks.