Infrared images hold significant value in applications such as remote sensing and fire safety. However, infrared detectors often face the problem of high hardware costs, which limits their widespread use. Advancements in deep learning have spurred innovative approaches to image super-resolution (SR), but comparatively few efforts have been dedicated to the exploration of infrared images. To address this, we design the Residual Swin Transformer and Average Pooling Block (RSTAB) and propose the SwinAIR, which can effectively extract and fuse the diverse frequency features in infrared images and achieve superior SR reconstruction performance. By further integrating SwinAIR with U-Net, we propose the SwinAIR-GAN for real infrared image SR reconstruction. SwinAIR-GAN extends the degradation space to better simulate the degradation process of real infrared images. Additionally, it incorporates spectral normalization, dropout, and artifact discrimination loss to reduce the potential image artifacts. Qualitative and quantitative evaluations on various datasets confirm the effectiveness of our proposed method in reconstructing realistic textures and details of infrared images.