Purpose: We propose a super-resolution (SR) method, named SR-CycleGAN, for SR of clinical computed tomography (CT) images to the micro-focus x-ray CT CT ( μ CT ) level. Due to the resolution limitations of clinical CT (about 500 × 500 × 500    μ m 3 / voxel ), it is challenging to obtain enough pathological information. On the other hand, μ CT scanning allows the imaging of lung specimens with significantly higher resolution (about 50 × 50 × 50    μ m 3 / voxel or higher), which allows us to obtain and analyze detailed anatomical information. As a way to obtain detailed information such as cancer invasion and bronchioles from preoperative clinical CT images of lung cancer patients, the SR of clinical CT images to the μ CT level is desired. Approach: Typical SR methods require aligned pairs of low-resolution (LR) and high-resolution images for training, but it is infeasible to obtain precisely aligned paired clinical CT and μ CT images. To solve this problem, we propose an unpaired SR approach that can perform SR on clinical CT to the μ CT level. We modify a conventional image-to-image translation network named CycleGAN to an inter-modality translation network named SR-CycleGAN. The modifications consist of three parts: (1) an innovative loss function named multi-modality super-resolution loss, (2) optimized SR network structures for enlarging the input LR image to 2 k -times by width and height to obtain the SR output, and (3) sub-pixel shuffling layers for reducing computing time. Results: Experimental results demonstrated that our method successfully performed SR of lung clinical CT images. SSIM and PSNR scores of our method were 0.54 and 17.71, higher than the conventional CycleGAN's scores of 0.05 and 13.64, respectively. Conclusions: The proposed SR-CycleGAN is usable for the SR of a lung clinical CT into μ CT scale, while conventional CycleGAN output images with low qualitative and quantitative values. More lung micro-anatomy information could be observed to aid diagnosis, such as the shape of bronchioles walls.